2. 下列计算错误的是(
A.$\sqrt{2} × \sqrt{8}=4$
B.$\sqrt{8} × \sqrt{6}=48$
C.$\sqrt{\dfrac{1}{3}} × \sqrt{18}=\sqrt{6}$
D.$\sqrt{\dfrac{5}{6}} × \sqrt{\dfrac{3}{10}}=\dfrac{1}{2}$
B
).A.$\sqrt{2} × \sqrt{8}=4$
B.$\sqrt{8} × \sqrt{6}=48$
C.$\sqrt{\dfrac{1}{3}} × \sqrt{18}=\sqrt{6}$
D.$\sqrt{\dfrac{5}{6}} × \sqrt{\dfrac{3}{10}}=\dfrac{1}{2}$
答案:2. B
3. 若$\sqrt{x(x-4)}=\sqrt{x} · \sqrt{x-4}$在实数范围内成立,则$x$的取值范围是(
A.$x ≥ 0$
B.$x ≤ 4$
C.$0 ≤ x ≤ 4$
D.$x ≥ 4$
D
).A.$x ≥ 0$
B.$x ≤ 4$
C.$0 ≤ x ≤ 4$
D.$x ≥ 4$
答案:3. D
4. 三角形的一边长是$\sqrt{42}\ \mathrm{cm}$,这一边上的高是$\sqrt{30}\ \mathrm{cm}$,这个三角形的面积是(
A.$6\sqrt{35}\ \mathrm{cm}^{2}$
B.$\sqrt{35}\ \mathrm{cm}^{2}$
C.$3\sqrt{35}\ \mathrm{cm}^{2}$
D.$2\sqrt{35}\ \mathrm{cm}^{2}$
C
).A.$6\sqrt{35}\ \mathrm{cm}^{2}$
B.$\sqrt{35}\ \mathrm{cm}^{2}$
C.$3\sqrt{35}\ \mathrm{cm}^{2}$
D.$2\sqrt{35}\ \mathrm{cm}^{2}$
答案:4. C
5. 计算:
(1) $-2\sqrt{15} × 4\sqrt{6}$;
(2) $-8\sqrt{35} × (-\dfrac{1}{4}\sqrt{1\dfrac{3}{7}})$;
(3) $6\sqrt{27xy} · \sqrt{\dfrac{x}{y}}\ (x ≥ 0,\ y > 0)$;
(4) $\sqrt{18mn} · \sqrt{2m^{2}n^{4}}\ (m ≥ 0,\ n ≥ 0)$.
(1) $-2\sqrt{15} × 4\sqrt{6}$;
(2) $-8\sqrt{35} × (-\dfrac{1}{4}\sqrt{1\dfrac{3}{7}})$;
(3) $6\sqrt{27xy} · \sqrt{\dfrac{x}{y}}\ (x ≥ 0,\ y > 0)$;
(4) $\sqrt{18mn} · \sqrt{2m^{2}n^{4}}\ (m ≥ 0,\ n ≥ 0)$.
答案:5. (1) $-24\sqrt{10}$; (2) $10\sqrt{2}$; (3) $18\sqrt{3}x$;
(4) $6mn^{2}\sqrt{mn}$.
(4) $6mn^{2}\sqrt{mn}$.