Question

Rationalize the denominator.

$\huge \tt \frac{ \sqrt{5} - \sqrt{3}} { \sqrt{5} + \sqrt{3}}$

​

Answer 1

Answer:

refer to the above attachment

Answer 2

The rationalized value of $\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$ is $\bold{4+\sqrt{15}}$

Step-by-step explanation:

To rationalize $\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$ multiply up and down by $(\sqrt{5}+\sqrt{3})$.

Therefore it becomes,

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

By formula, $\sf \fbox \orange{x^{2}-y^{2}=(x+y)(x-y)}$, substitute the formula in the above equation,  

Hence the equation becomes,

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

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

$= \frac{5 + 3 + 2 \sqrt{15} }{5 - 3}$

$= \frac{8 + 2 \sqrt{15} }{2}$

$= \frac{4 \sqrt{15} }{1}$

$\fbox \orange{= 4 \sqrt{15}}$

Learn more on brainly :-

Rationalizing Question/Answer ⤵️

• https://brainly.in/question/43298648

• https://brainly.in/question/43191745

Hope it helps ✌

$\huge\fbox \green{ \sf Thank You!!!}$