Question

Rút gọn

\(a.\sqrt{9\text{8}}-\sqrt{72}\text{+}\frac{\text{1}}{2}\sqrt{\text{8}}\)

b.\(\sqrt{\text{16}a}\text{+}2\sqrt{40a}-\text{3}\sqrt{90a}\)

c.\(\left(2\sqrt{\text{3}}\text{+}\sqrt{\text{5 }}\right)\sqrt{\text{3}}-\sqrt{\text{6}0}\)

Answer 1

a, \(=7\sqrt{2}-6\sqrt{2}+\frac{1}{2}.2\sqrt{2}=\sqrt{2}+\sqrt{2}=2\sqrt{2}\)

b, \(=4\sqrt{a}+4\sqrt{10a}-9\sqrt{10a}=4\sqrt{a}-5\sqrt{10a}\)

c, \(=6+\sqrt{15}-\sqrt{60}=6+\sqrt{15}-2\sqrt{15}=6-\sqrt{15}\)

Answer 2

Rút gọn

a) Ta có: \(\sqrt{98}-\sqrt{72}+\frac{1}{2}\sqrt{8}\)

\(=\sqrt{2}\left(\sqrt{49}-\sqrt{36}+\frac{1}{2}\sqrt{4}\right)\)

\(=\sqrt{2}\left(7-6+\frac{1}{2}\cdot2\right)\)

\(=\sqrt{2}\left(1+1\right)=2\sqrt{2}\)

b) Ta có: \(\sqrt{16a}+2\sqrt{40a}-3\sqrt{90a}\)

\(=\sqrt{a}\left(\sqrt{16}+2\sqrt{40}-3\sqrt{90}\right)\)

\(=\sqrt{a}\left(4+4\sqrt{10}-9\sqrt{10}\right)\)

\(=\sqrt{a}\left(4-5\sqrt{10}\right)\)

\(=4\sqrt{a}-5\sqrt{10a}\)

c) Ta có: \(\left(2\sqrt{3}+\sqrt{5}\right)\cdot\sqrt{3}-\sqrt{60}\)

\(=6+\sqrt{15}-\sqrt{60}\)

\(=6-\sqrt{15}\)