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一、把下列各式化成最简二次根式(直接写出结果)
1. $\sqrt{18} =$
2. $-\sqrt{72} =$
3. $\sqrt{25 × 22} =$
4. $\sqrt{\dfrac{49}{15}} =$
5. $\sqrt{2.5} =$
6. $\sqrt{2\dfrac{1}{12}} =$
7. $\sqrt{7^{-1}} =$
8. $\sqrt{18x^3y} =$
1. $\sqrt{18} =$
$3\sqrt{2}$
2. $-\sqrt{72} =$
$-6\sqrt{2}$
3. $\sqrt{25 × 22} =$
$5\sqrt{22}$
4. $\sqrt{\dfrac{49}{15}} =$
$\dfrac{7\sqrt{15}}{15}$
5. $\sqrt{2.5} =$
$\dfrac{\sqrt{10}}{2}$
6. $\sqrt{2\dfrac{1}{12}} =$
$\dfrac{5\sqrt{3}}{6}$
7. $\sqrt{7^{-1}} =$
$\dfrac{\sqrt{7}}{7}$
8. $\sqrt{18x^3y} =$
$3x\sqrt{2xy}$
$(x ≥ 0, y ≥ 0)$答案
1. $3\sqrt{2}$
2. $-6\sqrt{2}$
3. $5\sqrt{22}$
4. $\dfrac{7\sqrt{15}}{15}$
5. $\dfrac{\sqrt{10}}{2}$
6. $\dfrac{5\sqrt{3}}{6}$
7. $\dfrac{\sqrt{7}}{7}$
8. $3x\sqrt{2xy}$
2. $-6\sqrt{2}$
3. $5\sqrt{22}$
4. $\dfrac{7\sqrt{15}}{15}$
5. $\dfrac{\sqrt{10}}{2}$
6. $\dfrac{5\sqrt{3}}{6}$
7. $\dfrac{\sqrt{7}}{7}$
8. $3x\sqrt{2xy}$
二、把下列各式化成最简二次根式
9. $\sqrt{0.32}$
10. $\frac{3}{\sqrt{5}}$
11. $\sqrt{49 × 21}$
12. $\sqrt{\frac{1}{2} + \frac{1}{3}}$
13. $\frac{\sqrt{48}}{-2\sqrt{3}}$
14. $\sqrt{27b^3}\ (b ≥ 0)$
15. $\sqrt{\frac{27}{41^2 - 40^2}}$
16. $\sqrt{0.48(a^3b^2 + a^2b^3)}\ (a ≥ 0, b ≥ 0)$
9. $\sqrt{0.32}$
10. $\frac{3}{\sqrt{5}}$
11. $\sqrt{49 × 21}$
12. $\sqrt{\frac{1}{2} + \frac{1}{3}}$
13. $\frac{\sqrt{48}}{-2\sqrt{3}}$
14. $\sqrt{27b^3}\ (b ≥ 0)$
15. $\sqrt{\frac{27}{41^2 - 40^2}}$
16. $\sqrt{0.48(a^3b^2 + a^2b^3)}\ (a ≥ 0, b ≥ 0)$
答案
9. $\dfrac{2\sqrt{2}}{5}$
10. $\dfrac{3\sqrt{3}}{5}$
11. $7\sqrt{21}$
12. $\dfrac{\sqrt{30}}{6}$
13. $-2$
14. $3b\sqrt{3b}$
15. $\dfrac{\sqrt{3}}{3}$
16. $\dfrac{2\sqrt{3}}{5}ab\sqrt{a+b}$
10. $\dfrac{3\sqrt{3}}{5}$
11. $7\sqrt{21}$
12. $\dfrac{\sqrt{30}}{6}$
13. $-2$
14. $3b\sqrt{3b}$
15. $\dfrac{\sqrt{3}}{3}$
16. $\dfrac{2\sqrt{3}}{5}ab\sqrt{a+b}$
