Question

find the value of 8/sq. 3+sq.5 it is given that so. 3=1.732andsq.5=2.236

Answer 1

Heya friend,
Here is the answer you were looking for:
$\frac{8}{ \sqrt{3} + \sqrt{5} }$

On rationalizing the denominator we get,

$= \frac{8}{ \sqrt{3} + \sqrt{5} } \times \frac{ \sqrt{3} - \sqrt{5} }{ \sqrt{3} - \sqrt{5} }$

Using the identity :

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

$= \frac{8( \sqrt{3} - \sqrt{5} ) }{ {( \sqrt{3}) }^{2} - {( \sqrt{5} )}^{2} } \\ \\ = \frac{8 \sqrt{3} - 8 \sqrt{5} }{3 - 5} \\ \\ = \frac{8 \sqrt{3} - 8 \sqrt{5} }{ - 2} \\ \\ = \frac{ - 8 \sqrt{3} + 8 \sqrt{5} }{2} \\ \\ = - 4 \sqrt{3} + 4 \sqrt{5} \\ \\ = 4 \sqrt{5} - 4 \sqrt{3} \\ \\ = 4 \times 2.236 - 4 \times 1.732 \\ \\ = 8.944 - 6.928 \\ \\ = 2.016$

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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