Question

rationalise the denominator of 5/√7-√5​

Answer 1

Therefore we get ' ( 5√7 + 5√5 ) / 2 ' after rationalizing the denominator of 5/√7-√5.

Given:

Number = 5 / ( √7 - √5 )

To Find:

Rationalize the denominator of 5/√7-√5​

Solution:

This question has a simple solution as shown below.

Given number = 5/√7-√5​

Multiplying and dividing by √7 + √5

⇒ 5/√7-√5 = { 5 × (√7 + √5)} × { (√7-√5 ) × (√7 + √5 ) }

⇒ ( 5√7 + 5√5 ) / ( 7 - 5 )       { ∵ ( a + b ) ( a - b ) = a² - b² }

⇒ ( 5√7 + 5√5 ) / 2

Therefore we get ' ( 5√7 + 5√5 ) / 2 ' after rationalizing the denominator of 5/√7-√5.

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Answer 2

Answer:

$\frac{5(\sqrt{7} +\sqrt{5} )}{2 }$ is the  rationalization value of $\frac{5}{\sqrt{7} - \sqrt{5} }$ .

Step-by-step explanation:

Explanation:

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

Rationalization method - In order to remove radical symbols or fictitious numbers from the denominator of a rational function, rationalization typically refers to multiplying the function by a smart form of one.

Step 1:

We have $\frac{5}{\sqrt{7} - \sqrt{5} }$ ,

So, we  need to multiply  both numerator and denominator  with $\sqrt{7} + \sqrt{5}$

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

⇒$\frac{5(\sqrt{7} +\sqrt{5} )}{7 - 5 }$ =      $\frac{5(\sqrt{7} +\sqrt{5} )}{2 }$ .                     [  ∴ $a^2 - b^2 = (a + b)(a- b)$]

Final answer:

Hence, rationalization value of $\frac{5}{\sqrt{7} - \sqrt{5} }$ is $\frac{5(\sqrt{7} +\sqrt{5} )}{2 }$ .

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