Math, asked by aismem13, 11 months ago

$\sqrt{5} +\sqrt{2} / \sqrt{5} - \sqrt{2}$
rationalize the denominator

pls answer it !!! i will mark the brainliest !!

Answers

Answered by arshbbcommander

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

Rationalising factor..

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

Multiplying rationalising factor on both numerator and denominator...

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

using identity (a-b)(a+b)

$\frac{( \sqrt{5} + \sqrt{2} )^{2} }{ { \sqrt{5} }^{2} - \sqrt{2}^{2} } \\ = \frac{5 + 2 + 2 \sqrt{10} }{5 - 2} \\ = \frac{7 + 2 \sqrt{10}}{3}$

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...Hope it helps....

Answered by BrainlyIshika

$\dfrac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}$

Multiply both the numerator and denominator with $\sqrt{5}+\sqrt{2}$

$\dfrac{ \sqrt{5} + \sqrt{2} }{ \sqrt{5} - \sqrt{2} } \times \dfrac{ \sqrt{5} + \sqrt{2} }{ \sqrt{5} + \sqrt{2} } \\ \\ \frac{ {( \sqrt{5} + \sqrt{2}) }^{2} }{( \sqrt{5} - \sqrt{2})( \sqrt{5} + \sqrt{2} ) } \\ \\ \rm{\bold{Use \: the \: identities: }\: {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} } \\ \qquad \qquad \qquad \quad \: \: \rm(a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ \frac{ {( \sqrt{5} )}^{2} + 2( \sqrt{5} )( \sqrt{2}) + {( \sqrt{2}) }^{2} }{ ({{ \sqrt{5}) }^{2} - {( \sqrt{2}) }^{2} } } \\ \\ \frac{5 + 2 \sqrt{10} + 2 }{5 - 2} \\ \\ \fbox{\frac{7 + 2 \sqrt{10} }{3}}$

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rationalize the denominator pls answer it !!! i will mark the brainliest !!

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$\sqrt{5} +\sqrt{2} / \sqrt{5} - \sqrt{2}$
rationalize the denominator

pls answer it !!! i will mark the brainliest !!