Question

Rationalise the denominator of each of the following (i-vii):

(i) $\frac{3}{\sqrt{5}}$

(ii) $\frac{3}{2\sqrt{5}}$

(iii) $\frac{1}{\sqrt{12}}$

(iv) $\frac{\sqrt{2}}{\sqrt{5}}$

(v) $\frac{\sqrt{3}+1}{\sqrt{2}}$

(vi) $\frac{\sqrt{2}+\sqrt{5}}{3}$

(vii) $\frac{3\sqrt{2}}{\sqrt{5}}$

Answer 1

(i) We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Hence the given expression is simplified to.

(ii) We know that rationalization factor foris. We will multiply numerator and denominator of the given expression by, to get

Hence the given expression is simplified to.

(iii) We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Hence the given expression is simplified to.

(iv) We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Hence the given expression is simplified to.

(v) We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Hence the given expression is simplified to.

(vi) We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Hence the given expression is simplified to.

(vii) We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Hence the given expression is simplified to.