Question

Simplify 2 root 3-root 5 by 2root 2+3 root 3

Answer 1

I think this is answer

Answer 2

Concept

The elimination of radicals from an algebraic fraction's denominator is known as root rationalization in elementary algebra.

Given

Given that 2 root 3-root 5 by 2root 2+3 root 3

Find

We need to simplify $\frac{2\sqrt{3}-3\sqrt{5} }{2\sqrt{2}+3\sqrt{3} }$

Solution

To simplify the given equation we will rationalize the denominator

$\frac{2\sqrt{3}-3\sqrt{5} }{2\sqrt{2}+3\sqrt{3}}*\frac{2\sqrt{2}-3\sqrt{3}}{2\sqrt{2}-3\sqrt{3}}$

$\frac{4\sqrt{6}-18-2\sqrt{10}+3\sqrt{15}}{(2\sqrt{2})^2-(3\sqrt{3})^2}$  

In denominator we applied a^2-b^2

Now

$\frac{4\sqrt{6}-18-2\sqrt{10}+3\sqrt{15}}{8-27}\\\ \frac{18+2\sqrt{10}-4\sqrt{6}-3\sqrt{15}}{19}$

Hence the simplification is completed

#SPJ2