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7.$\sqrt{18}-\sqrt{32}+\sqrt{2}+\sqrt{3}=$
$\sqrt{3}$
.答案
7. $\sqrt{3}$
8. 若$\sqrt{8}$与最简二次根式$\sqrt{m + 1}$可以合并,则$m=$
1
.答案
8. 1
9. 若最简二次根式$\sqrt{3a + b}$与$\sqrt[a + b]{2b}$可以合并,则$a=$
$\dfrac{1}{2}$
, $b=$$\dfrac{3}{2}$
.答案
9. $\dfrac{1}{2}$；$\dfrac{3}{2}$
10. 计算.
(1)$\sqrt{27}-\sqrt{12}+\sqrt{\dfrac{1}{3}}$;
(2)$(\sqrt{24}+\sqrt{\dfrac{1}{2}})-(\sqrt{\dfrac{1}{8}}-\sqrt{6})$;
(3)$4\sqrt{\dfrac{1}{2}}+3\sqrt{\dfrac{1}{3}}-\sqrt{8}$;
(4)$\dfrac{2}{3}\sqrt{9x}+6\sqrt{\dfrac{x}{8}}-2x\sqrt{\dfrac{1}{x}}$;
(5)$8\sqrt{a}-b\sqrt{\dfrac{1}{a}}+\dfrac{1}{a^{2}}\sqrt{a^{3}b^{2}}(b＞0)$.
(1)$\sqrt{27}-\sqrt{12}+\sqrt{\dfrac{1}{3}}$;
(2)$(\sqrt{24}+\sqrt{\dfrac{1}{2}})-(\sqrt{\dfrac{1}{8}}-\sqrt{6})$;
(3)$4\sqrt{\dfrac{1}{2}}+3\sqrt{\dfrac{1}{3}}-\sqrt{8}$;
(4)$\dfrac{2}{3}\sqrt{9x}+6\sqrt{\dfrac{x}{8}}-2x\sqrt{\dfrac{1}{x}}$;
(5)$8\sqrt{a}-b\sqrt{\dfrac{1}{a}}+\dfrac{1}{a^{2}}\sqrt{a^{3}b^{2}}(b＞0)$.
答案
10. (1) $\dfrac{4\sqrt{3}}{3}$ (2) $3\sqrt{6}+\dfrac{\sqrt{2}}{4}$ (3) $\sqrt{3}$ (4) $\dfrac{3\sqrt{2x}}{2}$ (5) $8\sqrt{a}$
11. 计算.
$\sqrt{(1-\sqrt{2})^{2}}+\sqrt{(\sqrt{2}-\sqrt{3})^{2}}+\sqrt{(\sqrt{3}-\sqrt{4})^{2}}+···+\sqrt{(\sqrt{2025}-\sqrt{2026})^{2}}$
$\sqrt{(1-\sqrt{2})^{2}}+\sqrt{(\sqrt{2}-\sqrt{3})^{2}}+\sqrt{(\sqrt{3}-\sqrt{4})^{2}}+···+\sqrt{(\sqrt{2025}-\sqrt{2026})^{2}}$
答案
11. $\sqrt{2026}-1$
12. (2020·龙岗)
与$\sqrt{a^{3}b}$不能合并的是(
A.$\sqrt{\dfrac{b}{a}}$
B.$\sqrt{ab^{2}}$
C.$\sqrt{ab^{3}}$
D.$\sqrt{ab}$
与$\sqrt{a^{3}b}$不能合并的是(
B
)A.$\sqrt{\dfrac{b}{a}}$
B.$\sqrt{ab^{2}}$
C.$\sqrt{ab^{3}}$
D.$\sqrt{ab}$
答案
12. B
