Question

Answer 1

a: 10/căn 5

\(=2\sqrt{5}\cdot\dfrac{\sqrt{5}}{\sqrt{5}}=2\sqrt{5}\)

b: \(=\sqrt{\dfrac{10}{196}}=\dfrac{\sqrt{10}}{14}\)

c: \(\sqrt{\dfrac{11}{540}}=\dfrac{\sqrt{165}}{90}\)

d: \(\sqrt{\dfrac{\left(1-\sqrt{3}\right)^2}{27}}=\dfrac{\sqrt{3}-1}{3\sqrt{3}}=\dfrac{3-\sqrt{3}}{9}\)

e: \(ab\sqrt{\dfrac{a}{b}}=\dfrac{ab\sqrt{a}}{\sqrt{b}}=a\sqrt{ab}\)

f: \(=\sqrt{\dfrac{a^3}{4b}}=\sqrt{\dfrac{a^3b}{4b^2}}=a\cdot\dfrac{\sqrt{ab}}{2b}\)

g: \(=ab\cdot\sqrt{\dfrac{a^2b^2+1}{a^2b^2}}=\pm a^2b^2\pm1\)