Question

Rationalize the denominator of 30 divided by 5 square root 3 minus 3 square root 5 we need the answer but we have answer we need the explanation and so is 5 square root 3 + 3 square root 5 please answer

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{30}{5 \sqrt{3} - 3 \sqrt{5} }$

On rationalizing the denominator we get,

$= \frac{30}{5 \sqrt{3} - 3 \sqrt{5} } \times \frac{5 \sqrt{3} + 3 \sqrt{5} }{5 \sqrt{3} + 3 \sqrt{5} }$

Using the identity :

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


$= \frac{30(5 \sqrt{3} + 3 \sqrt{5} )}{ {(5 \sqrt{3} )}^{2} - {(3 \sqrt{5}) }^{2} } \\ \\ = \frac{150 \sqrt{3} + 90 \sqrt{5} }{75 - 45} \\ \\ = \frac{150 \sqrt{3} + 90 \sqrt{5} }{30} \\ \\ = 5 \sqrt{3} + 3 \sqrt{5}$

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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