The correct option is A 3 Given, #160; (√( 5 ) +√( 2 ) )(√( 5 ) √( 2 ) ) .We know, (a+b)(a b)=a^2 b^2 .Applying the identity, (√( 5 ) +√( 2 ...

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Rationalising Surds

Simplify: √...

Question

Simplify: $(\sqrt{5} - \sqrt{2}) (\sqrt{5} + \sqrt{2})$ .

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Solution

The correct option is A $3$
Given, $(\sqrt{5} + \sqrt{2}) (\sqrt{5} - \sqrt{2})$ .

We know, $(a + b) (a - b) = a^{2} - b^{2}$ .

Applying the identity,

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

$= (\sqrt{5})^{2} - (\sqrt{2})^{2} = 5 - 2 = 3$ .

Hence, $(\sqrt{5} + \sqrt{2}) (\sqrt{5} - \sqrt{2}) = 3$ .

Therefore, option $A$ is correct.

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