Question

simplify√7−√5/√7+√5​

Answer 1

Answer:

answer for the given problem is given

Answer 2

$\bf\large\underline\blue{Question:-}$

• Simplify $\frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} + \sqrt{5} }$

$\bf\large\underline\blue{Solution:-}$

$\frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} + \sqrt{5} }$

Now, we have to rationalise the denominator,

Rationalising the denominator means to remove all the surds from the denominator.

We get

$\frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} + \sqrt{5} }$

$\frac{ (\sqrt{7} - \sqrt{5} )}{ (\sqrt{7} + \sqrt{5} )} \times \frac{ (\sqrt{7} - \sqrt{5} ) }{( \sqrt{7} - \sqrt{5} )}$

$= \frac{ {( \sqrt{7} - \sqrt{5} )}^{2} }{ {( \sqrt{7} )}^{2} - {( \sqrt{5} )}^{2} }$

$= \frac{7 + 5 - 2 \times \sqrt{7} \times \sqrt{5} }{7 - 5}$

$= \frac{12 - 2 \sqrt{35} }{2}$

$= 6 - \sqrt{35}$

$\bf\large\underline\blue{Answer:-}$

• On Simplifying, we get $6 - \sqrt{35}$