Question

Rationalise the denominator of 1/root5 + root2

Answer 1

This is the solution.

Answer 2

Answer:

$\frac{1}{\sqrt{5}+\sqrt{2}}=\frac{\sqrt{5}-\sqrt{2}}{3}$

Step-by-step explanation:

$Rationalising\: the \: \\denominator \: of \: \frac{1}{\sqrt{5}+\sqrt{2}}$

Multiply numerator and denominator by (√5-√2), we get

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

=$\frac{\sqrt{5}-\sqrt{2}}{(\sqrt{5})^{2}-(\sqrt{2})^{2}}$

/* By algebraic identity:

(a+b)(a-b)=a²-b²*/

=$\frac{\sqrt{5}-\sqrt{2}}{5-2}$

=$\frac{\sqrt{5}-\sqrt{2}}{3}$

/* Denominator rationalised */

Therefore,

$\frac{1}{\sqrt{5}+\sqrt{2}}=\frac{\sqrt{5}-\sqrt{2}}{3}$

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