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1. $(\sqrt{2})^2=$
2
;$(-\sqrt{5})^2=$5
;$(2\sqrt{3})^2=$12
; $(-3\sqrt{2})^2=$18
.答案
1. $2,5,12,18$
2. $\sqrt{(-3)^2}=$
3
;$\sqrt{(\frac{1}{5})^2}=$$\frac{1}{5}$
;$\sqrt{(3-π)^2}=$$π-3$
;$\sqrt{10^{-4}}=$$\frac{1}{100}$
.答案
2. $3,\frac{1}{5},π-3,\frac{1}{100}$
3. 有下列算式:①$(\sqrt{6})^2=6$;②$\sqrt{(-3)^2}=-3$;③$(-\sqrt{5})^2=5$;④$\sqrt{4\frac{1}{9}}=\pm2\frac{1}{3}$.
其中正确的个数有
其中正确的个数有
2
个.答案
3. $2$
4. 利用$a=(\sqrt{a})^2(a≥0)$,把一个非负数写成另一个非负数的平方的形式:$5=$
$(\sqrt{5})^2$
;$\frac{1}{3}=$$(\sqrt{\frac{1}{3}})^2$
.答案
4. $(\sqrt{5})^2,(\sqrt{\frac{1}{3}})^2$
5. 计算:
(1)$\sqrt{(\sqrt{10}-\sqrt{6})^2}$; (2)$\sqrt{(π-4)^2}$; (3)$(-5\sqrt{2})^2$; (4)$(3\sqrt{\frac{5}{3}})^2$.
(1)$\sqrt{(\sqrt{10}-\sqrt{6})^2}$; (2)$\sqrt{(π-4)^2}$; (3)$(-5\sqrt{2})^2$; (4)$(3\sqrt{\frac{5}{3}})^2$.
答案
5. (1) $\sqrt{10}-\sqrt{6}$ (2)$4-π$ (3)$50$ (4)$15$
6. 若$\sqrt{(x-1)^2}=1-x$,则$x$的取值范围是
$x≤1$
.答案
6. $x≤1$
7. (1)若$\sqrt{3-x}$为整数,则正整数$x$的值是
(2)若$\sqrt{24n}$是整数,则正整数$n$的最小值是
$2$或$3$
;(2)若$\sqrt{24n}$是整数,则正整数$n$的最小值是
$6$
.答案
7.(1)$2$或$3$ (2)$6$
8. 计算:
(1)$\sqrt{2^2}+(-\sqrt{2})^2-2\sqrt{\frac{25}{4}}$; (2)$(-\sqrt{\frac{1}{7}})^2+\sqrt{\frac{16}{49}}+5\sqrt{(-\frac{2}{5})^2}$.
(1)$\sqrt{2^2}+(-\sqrt{2})^2-2\sqrt{\frac{25}{4}}$; (2)$(-\sqrt{\frac{1}{7}})^2+\sqrt{\frac{16}{49}}+5\sqrt{(-\frac{2}{5})^2}$.
答案
8.(1)$-1$ (2)$2\frac{5}{7}$
