Question

What is the following quotient? 5/ sqrt 11 - sqrt 3

Answer 1

Answer:

The correct option is b) $\frac{5\sqrt{11}+5\sqrt{3}}{8}$

Step-by-step explanation:

We need to find the quotient of $\frac{5}{\sqrt{11}-\sqrt{3}}$,

Rationalizing the above,

By multiply and divide by conjugate of its denominator,

$\frac{5}{\sqrt{11}-\sqrt{3}} \times \frac{\sqrt{11}+\sqrt{3}}{\sqrt{11}+\sqrt{3}}$

$\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}$

Since, $(a+b)(a-b)=a^{2}-b^{2}$

$\frac{5\sqrt{11}+5\sqrt{3}}{(11-3)}$

simplify,

$\frac{5\sqrt{11}+5\sqrt{3}}{8}$

Therefore, the correct option is b) $\frac{5\sqrt{11}+5\sqrt{3}}{8}$

Answer 2

 

$\displaystyle\\\frac{5}{\sqrt{11}-\sqrt{3}}=?\\\\\\\text{We rationalize the denominator.}\\\\\frac{5}{\sqrt{11}-\sqrt{3}}=\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}=\frac{5(\sqrt{11}+\sqrt{3})}{(11-3)}=\boxed{\bf\frac{5\sqrt{11}+5\sqrt{3})}{8}}$