Question

rationalise
$\frac{5 + \sqrt{2} }{ \sqrt{2} + 5}$
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Answer 1

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Q:-rationalise

$\frac{5 + \sqrt{2} }{ \sqrt{2} + 5 }$

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------>>>>Here is your answer<<<<--------

$⇒ \frac{5 + \sqrt{2} }{ \sqrt{2} + 5} \times \frac{ \sqrt{2} - 5}{ \sqrt{2} - 5}$

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

$⇒ \frac{5 \sqrt{2} - 25 + 2 - 5 \sqrt{2} }{2 - 25}$

$⇒ \frac{ - 25 + 2}{2 - 25} = \frac{ - 23}{- 23} = 1✓$

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Answer 2

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

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