Question

Rationalize it

(4√3+5√2) / (√48+√18)

pls do it step by step....
pls................​

Answer 1

: After rationalization, we have

$\frac{9+4\sqrt{6}}{15}$

Step-by-step explanation:

Since we have given that

$\frac{4\sqrt{3}+5\sqrt{2}}{\sqrt{48}+\sqrt{18}}$

First we will rewrite √48 as 4√3.

And √18 as 3√2.

So, we will get that

$\frac{4\sqrt{3}+5\sqrt{2} }{4\sqrt{3}+3\sqrt{2}}$

Now, we will rationalize the denominator :

$\frac{4\sqrt{3}+5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}\times \frac{4\sqrt{3}-3\sqrt{2}}{4\sqrt{3}-3\sqrt{2}}\\\\=\frac{48-12\sqrt{6}+20\sqrt{6}-30}{48-18}\\\\=\frac{18+8\sqrt{6}}{30}\\\\=\frac{9+4\sqrt{6}}{15}$

Hence, after rationalisation, we have

$\frac{9+4\sqrt{6}}{15}$