Question

7+3 root 5/3+root 5 -3-root5/3-root 5
simplify

Answer 1

hey friend here is your answer__________


this process is called rationalising the denomminator. refer to the attachment below. so the answer is 7

Answer 2

Heya friend,
Here is the answer you were looking for:
$\frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} }$

On rationalizing the denominator we get,


$= \frac{7 + 3 \sqrt{5} }{ 3 + \sqrt{5} } \times \frac{3 - \sqrt{5} }{3 - \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} }$

Using the identity :

$(x + y)(x - y) = {x}^{2} - {y}^{2}$

$= \frac{7(3 - \sqrt{5}) + 3 \sqrt{5}(3 - \sqrt{5} )}{ {(3)}^{2} - {( \sqrt{5}) }^{2} } - \frac{7(3 + \sqrt{5}) - 3 \sqrt{5} (3 + \sqrt{5}) }{ {(3)}^{2} - {( \sqrt{5} )}^{2} } \\ \\ = \frac{21 - 7 \sqrt{5} + 9 \sqrt{5} - 15}{9 - 5} - \frac{21 + 7 \sqrt{5} - 9 \sqrt{5} - 15}{9 - 5} \\ \\ = \frac{6 + 2 \sqrt{5} }{4} - \frac{6 - 2 \sqrt{5} }{4} \\ \\ = \frac{6 + 2 \sqrt{5} - 6 + 2 \sqrt{5} }{4} \\ \\ = \frac{4 \sqrt{5} }{4} \\ \\ = \sqrt{5}$


Hope this helps!!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
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