Question

rationalise the denominator in. √2/2+√2​

Answer 1

Correct Question:-

$\mathcal{Rationalise \: the \: denominator \: of} \: \: \: \frac{2}{2 + \sqrt{2} }$

What to do:-

$\mathrm{To \: rationalise \: the \: denominator.}$

Solution:-

Let's solve the problem

we have,

$\frac{2}{2 + \sqrt{2} }$

The denominator is 2+√2. Multiplying the numerator and denominator by 2-√2, We get

$⟹ \frac{2}{2 + \sqrt{2} } \times \frac{2 - \sqrt{2} }{2 - \sqrt{2} }$

$⟹ \frac{2(2 - \sqrt{2}) }{(2 + \sqrt{2} )(2 - \sqrt{2} )}$

⬤ Applying Algebraic Identity

(a+b)(a-b) = a² - b² to the denominator

We get,

$⟹ \frac{2(2 - \sqrt{2}) }{(2 {)}^{2} - ( \sqrt{2} {)}^{2} }$

$⟹ \frac{2(2 - \sqrt{2} )}{4 - 2}$

$⟹ \frac{ \cancel{2}(2 - \sqrt{2}) }{ \cancel{2}}$

$⟹2 - \sqrt{2}$

Hence, the denominator is rationalised.

Answer:-

$2 - \sqrt{2}$

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