Câu 3:

Tính

a) \(\frac{\sqrt{999}}{\sqrt{111}}\); b) \(\frac{\sqrt{52}}{\sqrt{\mathbf{1 1 7}}}\)

Lời giải:

a) \(\frac{\sqrt{999}}{\sqrt{111}}=\sqrt{\frac{999}{111}}=\sqrt{9}=3\)

b) \(\frac{\sqrt{52}}{\sqrt{117}}=\sqrt{\frac{52}{117}}=\sqrt{\frac{4}{9}}=\frac{2}{3}\)

Câu 4:

Rút gọn

a) \(\sqrt{\frac{2 a^{2} b^{4}}{50}}\)

b) \(\frac{\sqrt{2 a b^{2}}}{\sqrt{162}}\) với \(a \geq 0\)

Lời giải:

a) \(\sqrt{\frac{2 \mathrm{a}^{2} \mathrm{~b}^{4}}{50}}=\frac{\sqrt{\mathrm{a}^{2} \mathrm{~b}^{4}}}{\sqrt{25}}=\frac{\sqrt{\left(\mathrm{ab}^{2}\right)^{2}}}{5}=\frac{|\mathrm{a}| \mathrm{b}^{2}}{5}\)

b) \(\frac{\sqrt{2 \mathrm{ab}^{2}}}{\sqrt{162}}=\sqrt{\frac{2 \mathrm{ab}^{2}}{162}}=\sqrt{\frac{\mathrm{ab}^{2}}{81}}=\frac{|\mathrm{b}| \sqrt{\mathrm{a}}}{9}\)