Question

3 /sqrt3-11 rationalize the denominator

Answer 1

Answer:

The solved expression is $\frac{3}{\sqrt{3}-11}=-\frac{3\sqrt{3}+33}{118}$

Step-by-step explanation:

Given expression is $\frac{3}{\sqrt{3}-11}$

To rationalize the given expression as below :

$\frac{3}{\sqrt{3}-11}$

Multiply and divide the conjugate of denominator $\sqrt{3}-11$ is $\sqrt{3}+11$ we get

$=\frac{\frac{3}{\sqrt{3}-11}\times \sqrt{3}+11}{\sqrt{3}+11}$

$=\frac{3(\sqrt{3}+11)}{(\sqrt{3}-11)(\sqrt{3}+11)}$

$=\frac{3(\sqrt{3}+3(11)}{(\sqrt{3})^2-11^2}$  ( using the formula $(a-b)(a+b)=a^2-b^2$ )

$=\frac{3\sqrt{3}+33}{3-121}$

$=\frac{3\sqrt{3}+33}{-118}$

$=-\frac{3\sqrt{3}+33}{118}$

Therefore the solved expression is $-\frac{3\sqrt{3}+33}{118}$

Therefore the given expression is  $\frac{3}{\sqrt{3}-11}=-\frac{3\sqrt{3}+33}{118}$.