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1. (2025·宿豫期末)下列各式是最简二次根式的是(
A.$\sqrt{\dfrac{1}{5}}$
B.$\sqrt{15}$
C.$\sqrt{25}$
D.$\sqrt{45}$
B
)A.$\sqrt{\dfrac{1}{5}}$
B.$\sqrt{15}$
C.$\sqrt{25}$
D.$\sqrt{45}$
答案
1. B
2. (2025·锡山区期末)下列各式化成最简二次根式正确的是(
A.$\sqrt{\dfrac{24}{49}}=\dfrac{\sqrt{24}}{7}$
B.$\sqrt{\dfrac{3}{5}}=5\sqrt{15}$
C.$\sqrt{\dfrac{4}{7}}=\dfrac{2}{\sqrt{7}}$
D.$\sqrt{0.3}=\dfrac{\sqrt{30}}{10}$
D
)A.$\sqrt{\dfrac{24}{49}}=\dfrac{\sqrt{24}}{7}$
B.$\sqrt{\dfrac{3}{5}}=5\sqrt{15}$
C.$\sqrt{\dfrac{4}{7}}=\dfrac{2}{\sqrt{7}}$
D.$\sqrt{0.3}=\dfrac{\sqrt{30}}{10}$
答案
2. D
3. 若二次根式$\sqrt{a + 5}$是正整数，则负整数$a$可以是
-4 或 -1
.答案
3. -4 或 -1
4. 化简下列各式.
(1) $\sqrt{\dfrac{4}{3}}$；
(2) $\dfrac{1}{\sqrt{7}}$；
(3) $\sqrt{0.6}$；
(4) $\sqrt{\dfrac{3}{8}}$；
(5) $\sqrt{2\dfrac{1}{12}}$；
(6) $\sqrt{\dfrac{18}{a}}$.
(1) $\sqrt{\dfrac{4}{3}}$；
(2) $\dfrac{1}{\sqrt{7}}$；
(3) $\sqrt{0.6}$；
(4) $\sqrt{\dfrac{3}{8}}$；
(5) $\sqrt{2\dfrac{1}{12}}$；
(6) $\sqrt{\dfrac{18}{a}}$.
答案
4. (1) $\frac{2\sqrt{3}}{3}$ (2) $\frac{\sqrt{7}}{7}$ (3) $\frac{\sqrt{15}}{5}$ (4) $\frac{\sqrt{6}}{4}$ (5) $\frac{5\sqrt{3}}{6}$ (6) $\frac{3\sqrt{2a}}{a}$
5. 化简下列各式，使分母中不含根号.
(1) $\dfrac{3}{\sqrt{3}}$；
(2) $\dfrac{2}{\sqrt{6}}$；
(3) $\dfrac{\sqrt{3}}{\sqrt{54}}$；
(4) $\dfrac{\sqrt{5y}}{\sqrt{18x^{3}}}$；
(5) $\dfrac{\sqrt{8}}{\sqrt{2a}}$；
(6) $\dfrac{6a}{\sqrt{12a}}$.
(1) $\dfrac{3}{\sqrt{3}}$；
(2) $\dfrac{2}{\sqrt{6}}$；
(3) $\dfrac{\sqrt{3}}{\sqrt{54}}$；
(4) $\dfrac{\sqrt{5y}}{\sqrt{18x^{3}}}$；
(5) $\dfrac{\sqrt{8}}{\sqrt{2a}}$；
(6) $\dfrac{6a}{\sqrt{12a}}$.
答案
5. (1) $\sqrt{3}$ (2) $\frac{\sqrt{6}}{3}$ (3) $\frac{\sqrt{2}}{6}$ (4) $\frac{\sqrt{10xy}}{6x^{2}}$ (5) $\frac{2\sqrt{a}}{a}$ (6) $\sqrt{3a}$
6. (2025·姜堰期末)将二次根式$a\sqrt{-\dfrac{a + 2}{a^{2}}}$化为最简二次根式为(
A.$\sqrt{-a - 2}$
B.$-\sqrt{-a - 2}$
C.$\sqrt{a - 2}$
D.$-\sqrt{a - 2}$
B
)A.$\sqrt{-a - 2}$
B.$-\sqrt{-a - 2}$
C.$\sqrt{a - 2}$
D.$-\sqrt{a - 2}$
答案
6. B
