Question

simplify by rationalizing the denominator 5 / root 7 - root 5​

Answer 1

Step-by-step explanation:

i tried my best to help i dont know whether it is correct or wrong

Answer 2

Step-by-step explanation:

Given:-

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

What to to:-

To Rationalis the denominator.

Solution:-

Let's solve the problem

We have,

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

The denominator is √7-√5. Multiplying the numerator and denomination by √7+√5, we get

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

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

⬤ Applying Algebraic Identity

(a-b)(a+b) = a² - b² to the denominator

We get,

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

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

$⟹ \frac{5( \sqrt{7} + \sqrt{5} )}{2} \: \: Ans.$

Hence, the denominator is rationalised.

# Learn more:

Simplify by rstionalizing denominator 7+3 root 5/7 - root 5

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