Question

[nguyễn thu thảo]

Rút gọn :

a.\(\text{3}\sqrt{2}\text{+ }4\sqrt{\text{8}}-\sqrt{\text{1}\text{8}}\)

b.\(\sqrt{\text{3}}-\frac{\text{1}}{\text{3}}\sqrt{27}\text{+ }2\sqrt{\text{5}07}\)

c.\(\sqrt{2\text{5}a}\text{+ }\sqrt{49a}-\sqrt{\text{6}4a}\)

d.\(-\sqrt{\text{3}\text{6}b}\text{−}\frac{\text{1}}{\text{3}}\sqrt{\text{5}4b}\text{+}\frac{\text{1}}{\text{5}}\sqrt{\text{1}\text{5}0b}\)

Answer 1

[Nguyễn Lê Phước Thịnh]

a) Ta có: \(3\sqrt{2}+4\sqrt{8}-\sqrt{18}\)

\(=\sqrt{2}\left(3+4\cdot2-3\right)\)

\(=8\sqrt{2}\)

b) Ta có: \(\sqrt{3}-\frac{1}{3}\sqrt{27}+2\sqrt{507}\)

\(=\sqrt{3}\left(1-\frac{1}{3}\cdot\sqrt{9}+2\cdot\sqrt{169}\right)\)

\(=\sqrt{3}\left(1-1+26\right)\)

\(=26\sqrt{3}\)

c) Ta có: \(\sqrt{25a}+\sqrt{49a}-\sqrt{64a}\)

\(=\sqrt{25}\cdot\sqrt{a}+\sqrt{49}\cdot\sqrt{a}-\sqrt{64}\cdot\sqrt{a}\)

\(=\sqrt{a}\left(5+7-8\right)\)

\(=4\sqrt{a}\)

d) Ta có: \(-\sqrt{36b}-\frac{1}{3}\sqrt{54b}+\frac{1}{5}\sqrt{150b}\)

\(=-\sqrt{6b}\cdot\sqrt{6}-\frac{1}{3}\cdot\sqrt{6b}\cdot\sqrt{9}+\frac{1}{5}\cdot\sqrt{6b}\cdot\sqrt{25}\)

\(=-\sqrt{6b}\left(\sqrt{6}+1-1\right)\)

\(=-\sqrt{6b}\cdot\sqrt{6}=-6\sqrt{b}\)