Question

Rationalise the denominator 4 / √7 +√3

Answer 1

Answer:

$\sqrt{7} - \sqrt{3}$ is the required answer .

Step-by-step explanation:

Explanation:

Given , $\frac{4}{\sqrt{7} + \sqrt{3} }$

So the  denominator is $\sqrt{7} + \sqrt{3}$ given ,

Therefore , the conjugate of $\sqrt{7} + \sqrt{3}$ is $\sqrt{7} - \sqrt{3}$.

Conjugate ,a mathematical value or entity having a reciprocal relation with another.

Step 1:

We have , $\frac{4}{\sqrt{7} + \sqrt{3} }$

Now ,we multiply  both denominator and numerator by  $\sqrt{7} - \sqrt{3}$.

⇒$\frac{4}{\sqrt{7} + \sqrt{3} }$× $\frac{\sqrt{7} - \sqrt{3}}{\sqrt{7} - \sqrt{3}}$

⇒$\frac{4(\sqrt{7} - \sqrt{3})}{(\sqrt{7} )^{2} -(\sqrt{3} )^{2} }$            [∴$a^{2} -b^{2} = (a-b)(a+b)$]

⇒$\frac{4(\sqrt{7} - \sqrt{3})}{7-3 }$ = $\frac{4(\sqrt{7} - \sqrt{3})}{4 }$

⇒$\sqrt{7} - \sqrt{3}$

Final answer :

Hence , $\sqrt{7} - \sqrt{3}$ is the answer .

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