Question

Rationalise the denominator : 14/(5v3-v5)​

Answer 1

hope it helps you out!!

Answer 2

$\frac{5 \sqrt{3}+\sqrt{5}}{5}$

Solution:

Given expression : $\frac{14}{5\sqrt{3}-\sqrt{5} }$

To solve the given expression:

Rationalize the denominator means removing the square root terms in the denominator.

Rationalize the denominator of the expression  $\frac{14}{5\sqrt{3}-\sqrt{5} }$      

Multiply the numerator and denominator by the conjugate$5\sqrt{3}+\sqrt{5}$             $\frac{14}{5 \sqrt{3}-\sqrt{5}}=\frac{14}{5 \sqrt{3}-\sqrt{5}} \times \frac{5 \sqrt{3}+\sqrt{5}}{5 \sqrt{3}+\sqrt{5}}$    

Using the algebraic identity $(a-b)(a+b)=a^2-b^2$ in the denominator.

          $=\frac{14(5 \sqrt{3}+\sqrt{5})}{(5 \sqrt{3})^{2}-(\sqrt{5})^{2}}$

          $=\frac{14(5 \sqrt{3}+\sqrt{5})}{70}$  

Divide the numerator and denominator by 14, we get

          $=\frac{1(5 \sqrt{3}+\sqrt{5})}{5}$

         $=\frac{5 \sqrt{3}+\sqrt{5}}{5}$

Hence, the answer is $\frac{5 \sqrt{3}+\sqrt{5}}{5}$.

To learn more...

brainly.in/question/5471829