Svarlykill

Kafli 9

Undirbúningur

9.1.

ⓐ $81$ ⓑ $81$ ⓒ $- 81$

9.2.

$3.85$

9.3.

ⓐ $- \sqrt{100}$ ⓑ $\sqrt{- 100}$ .

9.4.

$\frac{5}{11}$

9.5.

$n^{6}$

9.6.

$\frac{1}{q^{8}}$

9.7.

ⓐ $12 x$ ⓑ $5 m + 5 n$

9.8.

$5 x \sqrt{2 x}$

9.9.

$24 u v$

9.10.

$72 - 42 n$

9.11.

$8 + 2 a + a^{2}$

9.12.

$\frac{30}{48}$

9.13.

$5$

9.14.

$49 - 9 x^{2}$

9.15.

ⓐ $3$ ⓑ $81$

9.16.

$22$

9.17.

$n = 2 eða n = 4$

9.18.

$y^{9}$

9.19.

$n^{12}$

9.20.

$x^{5}$

9.21.

$\frac{53}{60}$

9.22.

$64 x^{6} y^{15}$

9.23.

$\frac{1}{125}$

Prófið sjálf

9.1.

ⓐ $−7$ ⓑ $15$

9.2.

ⓐ $8$ ⓑ $−11$

9.3.

ⓐ ekki rauntala ⓑ $−9$

9.4.

ⓐ $−7$ ⓑ ekki rauntala

9.5.

ⓐ 7 ⓑ 5

9.6.

ⓐ 17 ⓑ $23$

9.7.

$6 < \sqrt{38} < 7$

9.8.

$9 < \sqrt{84} < 10$

9.9.

$\approx 3.32$

9.10.

$\approx 3.61$

9.11.

ⓐ $y^{4}$ ⓑ $z^{6}$

9.12.

ⓐ $m^{2}$ ⓑ $b^{5}$

9.13.

$8 x$

9.14.

$13 y$

9.15.

$−11 y$

9.16.

$−10 p$

9.17.

$10 a b$

9.18.

$15 m n$

9.19.

$7 x^{15}$

9.20.

$9 w^{18}$

9.21.

$13 x^{5} y^{7}$

9.22.

$12 p^{6} q^{10}$

9.23.

$4 \sqrt{3}$

9.24.

$3 \sqrt{5}$

9.25.

$12 \sqrt{2}$

9.26.

$12 \sqrt{3}$

9.27.

$b^{2} \sqrt{b}$

9.28.

$p^{4} \sqrt{p}$

9.29.

$4 x^{3} \sqrt{x}$

9.30.

$7 v^{4} \sqrt{v}$

9.31.

$4 y^{2} \sqrt{2 y}$

9.32.

$5 a^{4} \sqrt{3 a}$

9.33.

$7 a^{3} b^{2} {\sqrt{2 a b}}^{}$

9.34.

$6 m^{4} n^{5} \sqrt{5 m n}$

9.35.

$5 + 5 \sqrt{3}$

9.36.

$2 + 7 \sqrt{2}$

9.37.

$2 - \sqrt{3}$

9.38.

$2 - \sqrt{5}$

9.39.

$\frac{5}{4}$

9.40.

$\frac{7}{9}$

9.41.

$\frac{5}{4}$

9.42.

$\frac{7}{9}$

9.43.

$a$

9.44.

$x^{2}$

9.45.

$5 x^{2}$

9.46.

$6 z$

9.47.

$\frac{\sqrt{19}}{7}$

9.48.

$\frac{2 \sqrt{7}}{9}$

9.49.

$\frac{2 p \sqrt{6 p}}{7}$

9.50.

$\frac{2 x^{2} \sqrt{3 x}}{5}$

9.51.

$\frac{4 m \sqrt{5 m}}{n^{3}}$

9.52.

$\frac{3 u^{3} \sqrt{6 u}}{v^{4}}$

9.53.

$\frac{8 x^{2}}{3}$

9.54.

$\frac{2 a^{2}}{5}$

9.55.

$\frac{5 y \sqrt{x}}{6}$

9.56.

$\frac{4 m \sqrt{3}}{5 n^{3} \sqrt{5 n}}$

9.57.

$− \sqrt{2}$

9.58.

$−4 \sqrt{3}$

9.59.

$9 \sqrt{x}$

9.60.

$8 \sqrt{u}$

9.61.

$7 \sqrt{p} - 6 \sqrt{q}$

9.62.

$6 \sqrt{a} - 3 \sqrt{b}$

9.63.

$9 \sqrt{11}$

9.64.

$11 \sqrt{10}$

9.65.

$\sqrt{5} + 2 \sqrt{6}$

9.66.

$−5 \sqrt{7} + 2 \sqrt{5}$

9.67.

$−2 \sqrt{7 x}$

9.68.

$− \sqrt{3 y}$

9.69.

$−2 \sqrt{5 x y}$

9.70.

$0$

9.71.

$9 \sqrt{2}$

9.72.

$7 \sqrt{3}$

9.73.

$\sqrt{2}$

9.74.

$− \sqrt{5}$

9.75.

$6 \sqrt{3}$

9.76.

$−15 \sqrt{5}$

9.77.

$− \sqrt{3}$

9.78.

$0$

9.79.

$\frac{14}{15} \sqrt{2}$

9.80.

$\frac{1}{12} \sqrt{5}$

9.81.

$− m^{3} \sqrt{2 m}$

9.82.

$− p \sqrt{3 p}$

9.83.

$20 x \sqrt{2} - 12 x \sqrt{3}$

9.84.

$28 y \sqrt{3} - 24 y \sqrt{2}$

9.85.

$10 x \sqrt{3}$

9.86.

$−5 x \sqrt{2}$

9.87.

ⓐ $3 \sqrt{2}$ ⓑ $36 \sqrt{2}$

9.88.

ⓐ $5 \sqrt{2}$ ⓑ $90 \sqrt{2}$

9.89.

$12 \sqrt{15}$

9.90.

$27 \sqrt{2}$

9.91.

ⓐ $3 x^{2} \sqrt{2}$ ⓑ $10 y^{2} \sqrt{y}$

9.92.

ⓐ $2 x^{3} \sqrt{3}$ ⓑ $6 y^{3} \sqrt{y}$

9.93.

$144 x^{3} \sqrt{10}$

9.94.

$144 y^{2} \sqrt{5 y}$

9.95.

ⓐ 12 ⓑ $15$

9.96.

ⓐ 16 ⓑ 20

9.97.

ⓐ 330 ⓑ 200

9.98.

ⓐ 210 ⓑ 96

9.99.

ⓐ $6 - 2 \sqrt{5}$ ⓑ $2 \sqrt{3} - 3 \sqrt{6}$

9.100.

ⓐ $12 + 6 \sqrt{6}$ ⓑ $\sqrt{7} + 7 \sqrt{2}$

9.101.

ⓐ $18 + \sqrt{6}$ ⓑ $6 + 12 \sqrt{2}$

9.102.

ⓐ $−40 + 4 \sqrt{2}$ ⓑ $2 \sqrt{7} + 14 \sqrt{3}$

9.103.

$−3 + 2 \sqrt{6}$

9.104.

$−2 + 2 \sqrt{10}$

9.105.

$−66 + 15 \sqrt{7}$

9.106.

$41 - 14 \sqrt{11}$

9.107.

$1 + 9 \sqrt{21}$

9.108.

$−12 - 20 \sqrt{3}$

9.109.

$12 + 8 \sqrt{m} - 15 m$

9.110.

$10 - 47 \sqrt{n} - 15 n$

9.111.

ⓐ $102 + 20 \sqrt{2}$ ⓑ $55 + 6 \sqrt{6}$

9.112.

ⓐ $41 - 12 \sqrt{5}$ ⓑ $121 - 36 \sqrt{10}$

9.113.

$4 + 20 \sqrt{m} + 25 m$

9.114.

$9 - 24 \sqrt{n} + 16 n$

9.115.

$1$

9.116.

$−4$

9.117.

$−11$

9.118.

$−159$

9.119.

$\frac{\sqrt{2}}{2}$

9.120.

$\frac{\sqrt{3}}{3}$

9.121.

$\frac{4 - \sqrt{10}}{5}$

9.122.

$\frac{2 - \sqrt{3}}{4}$

9.123.

$\frac{2}{3}$

9.124.

$\frac{4}{3}$

9.125.

$r \sqrt{2}$

9.126.

$p^{2} \sqrt{7}$

9.127.

$\frac{5 s}{8}$

9.128.

$\frac{5 q^{2}}{6}$

9.129.

$\frac{9 x^{2}}{y^{2}}$

9.130.

$\frac{10 n^{3}}{m}$

9.131.

$\frac{5 \sqrt{3}}{3}$

9.132.

$\frac{6 \sqrt{5}}{5}$

9.133.

$\frac{\sqrt{5}}{2}$

9.134.

$- \frac{3 \sqrt{3}}{4}$

9.135.

$\frac{\sqrt{14}}{6}$

9.136.

$\frac{\sqrt{6}}{8}$

9.137.

$\frac{1}{3}$

9.138.

$\frac{\sqrt{5}}{5}$

9.139.

$\frac{2 (2 - \sqrt{3})}{1}$

9.140.

$\frac{5 (5 - \sqrt{3})}{22}$

9.141.

$- \frac{3 (1 + \sqrt{5})}{4}$

9.142.

$\frac{4 + \sqrt{6}}{5}$

9.143.

$\frac{\sqrt{5} (\sqrt{x} - \sqrt{2})}{x - 2}$

9.144.

$\frac{\sqrt{10} (\sqrt{y} + \sqrt{3})}{y - 3}$

9.145.

${\frac{(\sqrt{p} + \sqrt{2})}{p - 2}}^{2}$

9.146.

${\frac{(\sqrt{q} - \sqrt{10})}{q - 10}}^{2}$

9.147.

ⓐ nei ⓑ $já$

9.148.

ⓐ nei ⓑ $já$

9.149.

$10$

9.150.

$7$

9.151.

$\frac{23}{3}$

9.152.

$\frac{3}{10}$

9.153.

$\frac{1}{3}$

9.154.

$\frac{3}{5}$

9.155.

$engin lausn$

9.156.

$engin lausn$

9.157.

$2, 3$

9.158.

$5, 6$

9.159.

$7$

9.160.

$3$

9.161.

$\frac{127}{2}$

9.162.

$\frac{311}{3}$

9.163.

engin lausn

9.164.

engin lausn

9.165.

$engin lausn$

9.166.

$engin lausn$

9.167.

$engin lausn$

9.168.

$engin lausn$

9.169.

$19.2 fet$

9.170.

$52.0 cm$

9.171.

$9 sekúndur$

9.172.

$3.5 sekúndur$

9.173.

$42.7 mílur á klukkustund$

9.174.

$54.1 mílur á klukkustund$

9.175.

ⓐ 3 ⓑ 4 ⓒ 3

9.176.

ⓐ 10 ⓑ 2 ⓒ 2

9.177.

ⓐ $−5$ ⓑ ekki rauntala ⓒ $−2$

9.178.

ⓐ $−6$ ⓑ ekki rauntala ⓒ $−4$

9.179.

ⓐ $| b |$ ⓑ $w$ ⓒ $| m |$ ⓓ $q$

9.180.

ⓐ $| y |$ ⓑ $p$ ⓒ $| z |$ ⓓ $q$

9.181.

ⓐ $(u^{3})$ ⓑ $v^{5}$

9.182.

ⓐ $c^{4}$ ⓑ $d^{4}$

9.183.

ⓐ $3 x^{9}$ ⓑ $3 | q^{7} |$

9.184.

ⓐ $5 p^{3}$ ⓑ $3 q^{5}$

9.185.

ⓐ $| y | \sqrt[4]{y^{2}}$ ⓑ $z \sqrt[3]{z^{2}}$

9.186.

ⓐ $p \sqrt[5]{p^{3}}$ ⓑ $q^{2} \sqrt[6]{q}$

9.187.

ⓐ $3 \sqrt[3]{3}$ ⓑ $2 \sqrt[4]{4}$

9.188.

ⓐ $5 \sqrt[3]{5}$ ⓑ $3 \sqrt[4]{9}$

9.189.

ⓐ $3 p^{3} \sqrt[3]{2 p}$ ⓑ $2 q^{2} \sqrt[4]{4 q^{2}}$

9.190.

ⓐ $4 m^{3} \sqrt[3]{2 m^{2}}$ ⓑ $3 | n | \sqrt[4]{2 n^{3}}$

9.191.

ⓐ $−3 \sqrt[3]{4}$ ⓑ $ekki rauntala$

9.192.

ⓐ $−5 \sqrt[3]{5}$ ⓑ $ekki rauntala$

9.193.

ⓐ $| x |$ ⓑ $(y^{3})$

9.194.

ⓐ $m^{2}$ ⓑ $n^{2}$

9.195.

ⓐ $- \sqrt[3]{266}$ ⓑ $3 | m | \sqrt[4]{2 m^{2}}$

9.196.

ⓐ $−4$ ⓑ $3 | n | \sqrt[4]{2}$

9.197.

ⓐ $\frac{3 c^{3} \sqrt[3]{4 c}}{d^{2}}$ ⓑ $\frac{2 x^{2}}{| y |} \sqrt[4]{\frac{5 x^{2}}{y}}$

9.198.

ⓐ $2 r \sqrt[3]{\frac{5}{s}}$ ⓑ $\frac{3 (m^{3}) \sqrt[4]{2 m^{2}}}{| n^{3} |}$

9.199.

ⓐ $2 \sqrt[5]{3 x}$ ⓑ $2 \sqrt[3]{9}$

9.200.

ⓐ $2 \sqrt[4]{10 y}$ ⓑ $2 \sqrt[6]{32}$

9.201.

ⓐ $\sqrt[3]{3}$ ⓑ $6 \sqrt[4]{2}$

9.202.

ⓐ $− \sqrt[3]{2}$ ⓑ $5 \sqrt[5]{2}$

9.203.

ⓐ $2 y \sqrt[3]{4 y^{2}} + 3 y^{2} \sqrt[3]{4 y^{2}}$ ⓑ $3 r^{2} \sqrt[4]{3 r^{3}} + 4 r^{2} \sqrt[4]{3 r^{2}}$

9.204.

ⓐ $2 z^{2} \sqrt[3]{5 z} + 3 z \sqrt[3]{5 z}$ ⓑ $2 | s^{3} | \sqrt[4]{5 s} + 4 | s | \sqrt[4]{5 s^{2}}$

9.205.

ⓐ $\sqrt{t}$ ⓑ $\sqrt[3]{m}$ ⓒ $\sqrt[4]{r}$

9.206.

ⓐ $\sqrt{b}$ ⓑ $\sqrt[3]{z}$ ⓒ $\sqrt[4]{p}$

9.207.

ⓐ $s^{\frac{1}{2}}$ ⓑ $x^{\frac{1}{3}}$ ⓒ $b^{\frac{1}{4}}$

9.208.

ⓐ $v^{\frac{1}{2}}$ ⓑ $p^{\frac{1}{3}}$ ⓒ $p^{\frac{1}{4}}$

9.209.

ⓐ ${(10 m)}^{\frac{1}{2}}$ ⓑ ${(3 n)}^{\frac{1}{5}}$ ⓒ ${(486 y)}^{\frac{1}{4}}$

9.210.

ⓐ ${(3 k)}^{\frac{1}{7}}$ ⓑ ${(5 j)}^{\frac{1}{4}}$ ⓒ ${(1024 a)}^{\frac{1}{3}}$

9.211.

ⓐ 6 ⓑ 2 ⓒ 2

9.212.

ⓐ 10 ⓑ 3 ⓒ 3

9.213.

ⓐ $−5$ ⓑ $−5$ ⓒ $\frac{1}{5}$

9.214.

ⓐ $−2$ ⓑ $−2$ ⓒ $\frac{1}{2}$

9.215.

ⓐ ekki rauntala ⓑ $−8$ ⓒ $\frac{1}{8}$

9.216.

ⓐ ekki rauntala ⓑ $−4$ ⓒ $\frac{1}{4}$

9.217.

ⓐ $x^{\frac{5}{2}}$ ⓑ $z^{\frac{3}{4}}$ ⓒ $y^{\frac{2}{5}}$

9.218.

ⓐ $a^{\frac{2}{5}}$ ⓑ $b^{\frac{7}{3}}$ ⓒ $m^{\frac{5}{4}}$

9.219.

ⓐ 8 ⓑ 9 ⓒ 125

9.220.

ⓐ 32 ⓑ 729 ⓒ 8

9.221.

ⓐ $\frac{1}{32}$ ⓑ $\frac{1}{729}$ ⓒ $\frac{1}{8}$

9.222.

ⓐ $\frac{1}{8}$ ⓑ $\frac{1}{9}$ ⓒ $\frac{1}{125}$

9.223.

ⓐ $−64$ ⓑ $- \frac{1}{64}$ ⓒ ekki rauntala

9.224.

ⓐ $−729$ ⓑ $- \frac{1}{729}$ ⓒ ekki rauntala

9.225.

ⓐ 9 ⓑ $y^{3}$ ⓒ m

9.226.

ⓐ 25 ⓑ z ⓒ n

9.227.

ⓐ $p^{2}$ ⓑ $q^{6}$ ⓒ $x^{8}$

9.228.

ⓐ $r^{10}$ ⓑ $s^{9}$ ⓒ $m^{2}$

9.229.

ⓐ u ⓑ $v^{\frac{1}{5}}$ ⓒ $\frac{1}{x}$

9.230.

ⓐ $c^{2}$ ⓑ $\frac{1}{m}$ ⓒ $\frac{1}{d}$

9.231.

ⓐ $8 x^{\frac{1}{5}}$ ⓑ $4 y^{\frac{2}{9}}$

9.232.

ⓐ $64 m^{\frac{1}{2}}$ ⓑ $729 n^{\frac{3}{5}}$

9.233.

ⓐ $m^{2}$ ⓑ $n^{3}$

9.234.

ⓐ $u^{3}$ ⓑ $v^{5}$

Verkefni úr hluta 9.1

$−2$

11.

$−1$

13.

ekki rauntala

15.

ekki rauntala

17.

19.

21.

$8 < \sqrt{70} < 9$

23.

$14 < \sqrt{200} < 15$

25.

4.36

27.

7.28

29.

$y$

31.

$a^{7}$

33.

$7 x$

35.

$11 m^{10}$

37.

$9 x^{18}$

39.

$−9 x^{9}$

41.

$−8 a$

43.

$12 x y$

45.

$13 w^{4} y^{5}$

47.

$3 c^{4} d^{6}$

49.

25 sentimetrar

51.

Svör geta verið mismunandi.

Verkefni úr hluta 9.2

53.

$3 \sqrt{3}$

55.

$5 \sqrt{5}$

57.

$10 \sqrt{2}$

59.

$15 \sqrt{2}$

61.

$20 \sqrt{2}$

63.

$15 \sqrt{3}$

65.

$x^{3} \sqrt{x}$

67.

$p \sqrt{p}$

69.

$m^{6} \sqrt{m}$

71.

$r^{12} \sqrt{r}$

73.

$7 n^{8} \sqrt{n}$

75.

$9 r^{7} \sqrt{r}$

77.

$7 m^{2} \sqrt{2 m}$

79.

$5 r^{6} \sqrt{5 r}$

81.

$10 p^{6} \sqrt{2 p}$

83.

$11 m^{11} \sqrt{2 m}$

85.

$7 m^{3} n^{5} \sqrt{3 m n}$

87.

$5 r^{6} s^{4} \sqrt{3 r s}$

89.

$10 p^{4} q^{5} \sqrt{3 p q}$

91.

$11 m^{6} n^{10} \sqrt{2 m n}$

93.

$5 + 2 \sqrt{3}$

95.

$1 + 3 \sqrt{5}$

97.

$5 - \sqrt{6}$

99.

$1 + \sqrt{10}$

101.

$\frac{7}{8}$

103.

$\frac{11}{4}$

105.

$\frac{6}{7}$

107.

$\frac{3}{5}$

109.

$x^{2}$

111.

$\frac{1}{y^{2}}$

113.

$10 x^{2}$

115.

$4 p^{4}$

117.

$\frac{6}{\sqrt{35}}$

119.

$\frac{2 \sqrt{5}}{9}$

121.

$\frac{4 x^{3} \sqrt{6 x}}{11}$

123.

$\frac{5 m^{2} \sqrt{3 m}}{4}$

125.

$\frac{7 r^{2} \sqrt{2 r}}{10}$

127.

$\frac{2 q^{3} \sqrt{7}}{15}$

129.

$\frac{5 r^{4} \sqrt{3 r}}{s^{4}}$

131.

$\frac{2 p^{3} \sqrt{7 p}}{q}$

133.

$\frac{5 x}{3}$

135.

$\frac{11 p \sqrt{p}}{9}$

137.

$\frac{4 x y}{3}$

139.

$\frac{1}{2 p q \sqrt{p}}$

141.

ⓐ $17.0 fet$ ⓑ $12.0 fet$

143.

Svör geta verið mismunandi.

Verkefni úr hluta 9.3

145.

$3 \sqrt{2}$

147.

$9 \sqrt{5}$

149.

$− \sqrt{7}$

151.

$9 \sqrt{y}$

153.

$−3 \sqrt{a}$

155.

$7 \sqrt{c}$

157.

$8 \sqrt{a} - 2 \sqrt{b}$

159.

$5 \sqrt{m} + \sqrt{n}$

161.

$13 \sqrt{7}$

163.

$−3 \sqrt{11}$

165.

$−5 \sqrt{3} + 7 \sqrt{5}$

167.

$8 \sqrt{2} - 3 \sqrt{5}$

169.

$4 \sqrt{2 a}$

171.

$\sqrt{3 c}$

173.

$4 \sqrt{3 a b}$

175.

$\sqrt{p q}$

177.

$9 \sqrt{2}$

179.

$\sqrt{5}$

181.

$−2 \sqrt{3}$

183.

$7 \sqrt{3}$

185.

$−8 \sqrt{2}$

187.

$16 \sqrt{3}$

189.

$5 \sqrt{2}$

191.

$− \sqrt{5}$

193.

$− \sqrt{3}$

195.

$- \frac{11}{12} \sqrt{2}$

197.

$a^{2} \sqrt{2 a}$

199.

$2 c^{3} \sqrt{5 c}$

201.

$36 p^{2} \sqrt{5} - 42 p^{2} \sqrt{2}$

203.

$10 r^{4} \sqrt{2} + 12 r^{4} \sqrt{6}$

205.

$14 x \sqrt{5}$

207.

$4 y \sqrt{2}$

209.

$6 \sqrt{2}$

211.

$2 k^{2} \sqrt{7}$

213.

$2 \sqrt{3}$

215.

$\sqrt{2}$

217.

$\sqrt{13}$

219.

$a^{2} \sqrt{5 a}$

221.

$19 \sqrt{19}$

223.

$5 \sqrt{3}$

225.

$− \sqrt{3}$

227.

$8 x \sqrt{6}$

229.

$124.5 tommur$

231.

Svör geta verið mismunandi.

Verkefni úr hluta 9.4

233.

ⓐ $4$ ⓑ $18 \sqrt{6}$

235.

ⓐ $7 \sqrt{2}$ ⓑ 160

237.

$30 \sqrt{3}$

239.

$−18 \sqrt{6}$

241.

$−30 \sqrt{2}$

243.

$28 \sqrt{2}$

245.

ⓐ $5 y^{2} \sqrt{3}$ ⓑ $6 n^{2} \sqrt{n}$

247.

ⓐ $8 y^{3} \sqrt{2}$ ⓑ $11 s^{3} \sqrt{s}$

249.

$40 b^{2} \sqrt{3}$

251.

$150 d^{5}$

253.

$54 y^{4} \sqrt{y}$

255.

$−96 k^{5} \sqrt{k}$

257.

ⓐ 11 ⓑ 21

259.

ⓐ 23 ⓑ 3

261.

ⓐ −234 ⓑ 180

263.

ⓐ $105 \sqrt{2}$ ⓑ 56

265.

ⓐ $24 - 4 \sqrt{11}$ ⓑ $5 \sqrt{2} - 2 \sqrt{6}$

267.

ⓐ $−14 - 7 \sqrt{11}$ ⓑ $6 \sqrt{7} - 7 \sqrt{2}$

269.

ⓐ $44 + 8 \sqrt{11}$ ⓑ $15$

271.

ⓐ $18 - 5 \sqrt{2}$ ⓑ $\sqrt{21} - 7 \sqrt{3}$

273.

$60 + 2 \sqrt{3}$

275.

$52 + 3 \sqrt{2}$

277.

$27 - 9 \sqrt{7}$

279.

$−62 + 55 \sqrt{5}$

281.

$41 + 7 \sqrt{55}$

283.

$−81 + 44 \sqrt{78}$

285.

$18 + 7 \sqrt{w} - w$

287.

$66 + 73 \sqrt{n} + 15 n$

289.

ⓐ $27 + 8 \sqrt{11}$ ⓑ $29 - 12 \sqrt{5}$

291.

ⓐ $35 - 10 \sqrt{10}$ ⓑ $82 + 48 \sqrt{2}$

293.

295.

297.

$−127$

299.

301.

$−24 \sqrt{3}$

303.

$−210 \sqrt{3}$

305.

$7 y^{3} \sqrt{5}$

307.

$29$

309.

$29 - 7 \sqrt{17}$

311.

ⓐ $4.6 fet$ ⓑ $21 ferfet$

313.

$31.9 ferningur jardar$

315.

ⓐ Þegar neikvæð tala er hafin í annað veldi verður útkoman jákvæð. ⓑ Þar sem mínusmerkið er ekki innan svigans er það ekki hluti af veldinu og talan helst neikvæð.

Verkefni úr hluta 9.5

317.

$\frac{\sqrt{3}}{2}$

319.

$\frac{2 \sqrt{2}}{3}$

321.

$\frac{1 - 2 \sqrt{2}}{4}$

323.

$\frac{2 + \sqrt{5}}{2}$

325.

$\frac{4}{5}$

327.

$\frac{4}{3}$

329.

ⓐ $2 x^{2}$ ⓑ $\frac{10 m^{2}}{7}$

331.

$\frac{5 r}{6}$

333.

$\frac{6 p \sqrt{102}}{q^{2}}$

335.

$\frac{8 n}{3 m^{3}}$

337.

$\frac{\sqrt{2}}{2}$

339.

$\frac{1 + \sqrt{5}}{3}$

341.

$\frac{4}{5}$

343.

$y^{3} \sqrt{13}$

345.

$\frac{5 \sqrt{6}}{3}$

347.

$\frac{6 \sqrt{7}}{7}$

349.

$\frac{3 \sqrt{13}}{13}$

351.

$\frac{\sqrt{10}}{3}$

353.

$\frac{4 \sqrt{5}}{45}$

355.

$- \frac{3 \sqrt{3}}{2}$

357.

$\frac{\sqrt{15}}{10}$

359.

$\frac{\sqrt{70}}{20}$

361.

$\frac{\sqrt{133}}{35}$

363.

ⓐ $\frac{3 (3 - \sqrt{11})}{−2}$ ⓑ $−2 (1 + \sqrt{5})$

365.

ⓐ $\frac{5 (5 - \sqrt{6})}{19}$ ⓑ $3 (3 + \sqrt{7})$

367.

$\frac{\sqrt{3} (\sqrt{m} + \sqrt{5})}{m - 5}$

369.

$\frac{\sqrt{2} (\sqrt{x} + \sqrt{6})}{x - 6}$

371.

${\frac{(\sqrt{r} + \sqrt{5})}{r - 5}}^{2}$

373.

$\frac{5 y^{2}}{x}$

375.

$3 \sqrt{5}$

377.

$\frac{2 \sqrt{3}}{9}$

379.

$\frac{3 (5 - \sqrt{5})}{20}$

381.

$\frac{\sqrt{2} (\sqrt{x} + \sqrt{3})}{x - 3}$

383.

${\frac{(\sqrt{x} + 2 \sqrt{2})}{x - 8}}^{2}$

385.

$\frac{5 \sqrt{10}}{4} sekúndur$

387.

Svör geta verið mismunandi.

Verkefni úr hluta 9.6

389.

ⓐ $já$ ⓑ $nei$

391.

ⓐ nei ⓑ já

393.

395.

397.

399.

$17$

401.

$\frac{13}{5}$

403.

$\frac{5}{2}$

405.

$engin lausn$

407.

$engin lausn$

409.

ⓐ $10, 11$ ⓑ $5$

411.

ⓐ $8, 9$ ⓑ $11$

413.

$3$

415.

$5$

417.

ekki rauntala

419.

$\frac{1}{4}$

421.

ⓐ $engin lausn$ ⓑ $\frac{57}{16}$

423.

ⓐ $engin lausn$ ⓑ 6

425.

engin lausn

427.

429.

431.

$11.4 fet$

433.

$8 sekúndur$

435.

$15.8 sekúndur$

437.

$72 mílur á klukkustund$

439.

$53.0 mílur á klukkustund$

441.

Svör geta verið mismunandi.

Verkefni úr hluta 9.7

443.

445.

447.

449.

451.

ⓐ $a$ ⓑ $| b |$

453.

ⓐ $| k |$ ⓑ $| p |$

455.

ⓐ $a^{2}$ ⓑ $b^{9}$

457.

ⓐ $r^{2}$ ⓑ $s^{10}$

459.

ⓐ $−2 c^{3}$ ⓑ $5 d^{5}$

461.

ⓐ $2 r^{2}$ ⓑ $3 s^{6}$

463.

ⓐ $u \sqrt[5]{u^{2}}$ ⓑ $(v) \sqrt[6]{v^{5}}$

465.

ⓐ $p \sqrt[5]{p^{3}}$ ⓑ $q^{2} \sqrt[3]{q^{2}}$

467.

ⓐ $5 \sqrt[3]{5}$ ⓑ $2 \sqrt[6]{2}$

469.

ⓐ $5 \sqrt[4]{5}$ ⓑ $3 \sqrt[3]{3}$

471.

ⓐ $2 a \sqrt[5]{3 a^{2}}$ ⓑ $5 b \sqrt[3]{3 b}$

473.

ⓐ $8 p \sqrt[3]{p^{2}}$ ⓑ $3 (q) \sqrt[4]{4 q^{3}}$

475.

ⓐ $−3 \sqrt[5]{2}$ ⓑ $ekki rauntala$

477.

ⓐ $−2$ ⓑ $ekki rauntala$

479.

ⓐ $d$ ⓑ $| m |$

481.

ⓐ $r^{3}$ ⓑ $| c^{3} |$

483.

ⓐ $−5$ ⓑ $2 (m) \sqrt[4]{m^{2}}$

485.

ⓐ $3 \sqrt[3]{6}$ ⓑ $2 | r | \sqrt[4]{2 r^{3}}$

487.

ⓐ $2 r^{2} \sqrt[5]{\frac{3 r}{s^{3}}}$ ⓑ $2 (u) \sqrt[6]{\frac{2 u}{v^{3}}}$

489.

ⓐ $\frac{5 u^{3} \sqrt[3]{5 u}}{v}$ ⓑ $\frac{3 (c^{5}) \sqrt[4]{9 c}}{d^{2}}$

491.

ⓐ $2 \sqrt[3]{15 q}$ ⓑ $−4 \sqrt[4]{27}$

493.

ⓐ

ⓑ

495.

ⓐ $2 \sqrt[3]{2}$ ⓑ $−2 \sqrt[4]{3}$

497.

ⓐ $3 \sqrt[4]{3} + 5 \sqrt[4]{2}$ ⓑ $13 \sqrt[3]{2}$

499.

ⓐ $2 b \sqrt[3]{10 b^{2}} + 3 b \sqrt[3]{10}$ ⓑ $2 v^{2} \sqrt[4]{10 v^{2}} - 4 \sqrt[4]{5 v^{3}}$

501.

$2$

503.

$| b |$

505.

$5 d^{5}$

507.

$s^{2} \sqrt[4]{s^{2}}$

509.

$2 (y) \sqrt[4]{3 y^{2}}$

511.

$ekki rauntala$

513.

$2 x \sqrt[5]{2 x}$

515.

$2 (u) \sqrt[6]{\frac{2 u}{v^{3}}}$

517.

$2 \sqrt[4]{2}$

519.

$3 │ u │ \sqrt[4]{6 u^{3}} + 4 \sqrt[4]{3 u^{3}}$

521.

$5$

523.

Svör geta verið mismunandi.

Verkefni úr hluta 9.8

525.

527.

529.

531.

533.

535.

537.

ⓐ 5 ⓑ 3 ⓒ 2

539.

ⓐ 6 ⓑ 2 ⓒ 3

541.

543.

545.

547.

549.

551.

553.

555.

557.

559.

561.

563.

565.

567.

569.

571.

573.

575.

577.

579.

ⓐ $3 r^{\frac{1}{5}}$ ⓑ $2 s^{\frac{1}{14}}$

581.

ⓐ $9 m^{\frac{1}{2}}$ ⓑ $125 n^{2}$

583.

ⓐ $r^{2} s$ ⓑ $u^{3} v^{4}$

585.

ⓐ $r^{8} s^{5}$ ⓑ $u^{8} v^{4}$

587.

ⓐ $a^{3}$ ⓑ $b^{4}$

589.

ⓐ $m$ ⓑ $n^{2}$

591.

$n$

593.

$b^{6}$

595.

$\frac{1}{z^{2}}$

597.

$2 s^{\frac{1}{10}}$

599.

$u^{2} v^{3}$

601.

15.6 fet

603.

8 sekúndur

605.

Svör geta verið mismunandi.

Upprifjunarverkefni

607.

609.

$−9$

611.

ekki rauntala

613.

615.

$12 < \sqrt{155} < 13$

617.

7.55

619.

$8 (b)$

621.

$15 (m) (n)$

623.

$7 (y)$

625.

$11 (c) (d)$

627.

$7 \sqrt{2}$

629.

$(y^{9}) \sqrt{y}$

631.

$6 n^{6} \sqrt{n}$

633.

$5 (n^{3}) \sqrt{6 n}$

635.

$6 r^{2} (s) \sqrt{3 r s}$

637.

$1 + \sqrt{2}$

639.

$\frac{3}{2}$

641.

$y^{2}$

643.

$6 q^{2}$

645.

$\frac{\sqrt{26}}{13}$

647.

$\frac{3 r^{2} \sqrt{r}}{2}$

649.

$\frac{2 (r) (s^{3}) \sqrt{r}}{5}$

651.

$12 \sqrt{5}$

653.

$4 \sqrt{m}$

655.

$11 \sqrt{13} + 2 \sqrt{3}$

657.

$3 \sqrt{3 r s} - 5 \sqrt{r s}$

659.

$5 \sqrt{2}$

661.

$9 \sqrt{3}$

663.

$0$

665.

$17 n^{2} \sqrt{2}$

667.

$24 \sqrt{7}$

669.

$180 y^{2}$

671.

673.

675.

$20 - 10 \sqrt{7}$

677.

$13 - 2 \sqrt{2}$

679.

$5 - 13 \sqrt{x} - 6 x$

681.

$1 + 12 \sqrt{p} + 36 p$

683.

$−19$

685.

$\frac{\sqrt{3}}{2}$

687.

$\frac{4}{3}$

689.

$y^{2} \sqrt{10}$

691.

$\frac{2 \sqrt{15}}{3}$

693.

$\frac{\sqrt{5}}{3}$

695.

$\frac{\sqrt{21}}{14}$

697.

$\frac{16 - 12 \sqrt{3}}{−11}$

699.

$−8 - 4 \sqrt{5}$

701.

$\frac{\sqrt{2 p} - \sqrt{6}}{p - 3}$

703.

705.

$\frac{7}{2}$

707.

4 og 5

709.

711.

$\frac{43}{2}$

713.

715.

$\frac{1}{16}$

717.

719.

7.5 sekúndur

721.

ⓐ 2 ⓑ 4

723.

ⓐ $d$ ⓑ $| v |$

725.

ⓐ $2 x^{2}$ ⓑ $2 y^{2}$

727.

ⓐ $d$ ⓑ $m \sqrt[11]{m^{6}}$

729.

ⓐ $2 c \sqrt[5]{2 c^{3}}$ ⓑ $2 (d) \sqrt[4]{3 d^{3}}$

731.

ⓐ $−5 \sqrt[3]{4}$ ⓑ ekki rauntala

733.

$w^{3} \sqrt[3]{w}$

735.

$3 z^{2}$

737.

$2 \sqrt[5]{20}$

739.

$2 \sqrt[4]{2}$

741.

$2 t \sqrt[5]{3 t^{3}} + 3 \sqrt[5]{2 t^{4}}$

743.

745.

$v^{\frac{1}{6}}$

747.

${(10 z)}^{\frac{1}{6}}$

749.

751.

$\frac{1}{5}$

753.

$\frac{1}{6}$

755.

$n^{\frac{8}{5}}$

757.

32,768

759.

$\frac{1}{59,049}$

761.

$x^{8}$

763.

$2 s^{\frac{9}{16}}$

765.

$z^{2}$

Æfingapróf

767.

$13 m^{2} | n |$

769.

$4 \sqrt{13} + 5 \sqrt{2}$

771.

$60 y^{2} \sqrt{3}$

773.

$1 - 4 \sqrt{q} + 4 q$

775.

ⓐ $3 (x^{3})$ ⓑ $2 (y^{3})$

777.

$(y) \sqrt{2}$

779.

$0$

781.

343

783.

$\frac{1}{w}$

785.

$\frac{\sqrt{6}}{4}$

787.

789.

6.1 sekúndur