Question

5√3 + 3√5 /5√3 - 3√5
Simplify​

Answer 1

Step-by-step explanation:

Given,

$\dfrac{5 \sqrt{3} + 3 \sqrt{5} }{5 \sqrt{3} - 3 \sqrt{5} }$

To Do :-

Simplify it

Solution :-

We can simplify the above fraction by Rationalising the Denominater.

What is Rationalising the Denominater ?

We can observe the denominator of the above fraction is an irrational number So Multiplying Denominater and Numerator with its Rationalising factor We will get the rational form of denominater.

Let's do :-

Rationalising factor of $\sf "5\sqrt{3}-3\sqrt{5}\: is \: "5\sqrt{3}+3\sqrt{5}$

$\dfrac{5 \sqrt{3} + 3 \sqrt{5} }{5 \sqrt{3} - 3 \sqrt{5} } \times \dfrac{5 \sqrt{3} + 3 \sqrt{5} }{5 \sqrt{3} + 3 \sqrt{5} }$

$\dfrac{ {(5 \sqrt{3} + 3 \sqrt{5}) }^{2} }{( {5 \sqrt{3}) }^{2} - ( {3} \sqrt{5}) ^{2} }$

$\dfrac{( {5 \sqrt{3} )}^{2} + 2(5 \sqrt{3})(3 \sqrt{5}) + ( {3} \sqrt{5}) ^{2} }{75 - 45}$

$\dfrac{75 + 45 + 30 \sqrt{15} }{30}$

$\dfrac{15(5 + 3 + 2 \sqrt{15}) }{15 \times 2}$

$\dfrac{8 + 2 \sqrt{15} }{2}$

$\dfrac{2(4 + \sqrt{15}) }{2}$

$4 + \sqrt{15}$