Question

Find the values of each of the following correct to three places of decimals, it being given that $\sqrt{2}=1.4142,$ $\sqrt{3}=1.732$, $\sqrt{5}=2.2360,$ $\sqrt{6}=2.4495$ and $\sqrt{10}=3.162$,

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

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

Answer 1

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

Putting the values of, we get

Hence the given expression is simplified to.

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

Putting the value of, we get

Hence the given expression is simplified to.