Question

rationalize the denominator 3/√7+√2​

Answer 1

Answer:

(3√7 - 3√3)/5

Step-by-step explanation:

For rationalizing the denominator, multiply both numerator and denominator by the conjugate of the denominator.

Here, the conjugate of denominator is √7 - √2

$\hookrightarrow \: \sf{\dfrac{3}{\sqrt{7}+\sqrt{2}}\times\dfrac{\sqrt{7}-\sqrt{2}}{\sqrt{7}-\sqrt{2}}}$

Use the identity (a - b) (a + b) = a² - b²

$\implies \sf{\dfrac{3(\sqrt{7}-\sqrt{2})}{(\sqrt{7})^{2}-(\sqrt{2})^2}}$

$\implies \sf{\dfrac{3\sqrt{7}-3\sqrt{2}}{7-2}}$

$\implies \sf{\dfrac{3\sqrt{7}-3\sqrt{2}}{5}}$

So, the answer would be:

$\boxed{\bf{\dfrac{3\sqrt{7}-3\sqrt{2}}{5}}}$