Question

find the value if
$\sqrt{5} = 2.236$

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{ \sqrt{5} + \sqrt{2} }{ \sqrt{5} - \sqrt{2} } \\ \\ on \: rationalizing \: we \: get \\ \\ = \frac{ \sqrt{5} + \sqrt{2} }{ \sqrt{5} - \sqrt{2} } \times \frac{ \sqrt{5} + \sqrt{2} }{ \sqrt{5} + \sqrt{2} } \\ \\ using \: the \: identities \\ \\ {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{ {( \sqrt{5}) }^{2} + {( \sqrt{2}) }^{2} + 2 \times \sqrt{5} \times \sqrt{2} }{ {( \sqrt{5}) }^{2} - {( \sqrt{2}) }^{2} } \\ \\ = \frac{5 + 2 + 2 \sqrt{10} }{5 - 2} \\ \\ = \frac{7 + 2 \sqrt{5} \times \sqrt{2} }{3} \\ \\ = \frac{7 + 2 \times 2.236 \times 1.414}{3} \\ \\ = \frac{7 + 6.323}{3} \\ \\ = \frac{13.323}{3}$


Hope this helps!!!

@Mahak24

Thanks...
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