Question

rationalize denominator 2√3-√5/2√2+3√3​

Answer 1

Answer:

here is your answer with full explanation

Answer 2

ANSWER:

To Rationalize:

• (2√3 - √5)/(2√2 + 3√3)

Solution:

We are given that,

$\implies\dfrac{2\sqrt3-\sqrt5}{2\sqrt2+3\sqrt3}$

Multiplying and dividing by (2√2 - 3√3),

$\implies\dfrac{2\sqrt3-\sqrt5}{2\sqrt2+3\sqrt3}\times\dfrac{2\sqrt2-3\sqrt3}{2\sqrt2-3\sqrt3}$

So,

$\implies\dfrac{(2\sqrt3-\sqrt5)(2\sqrt2-3\sqrt3)}{(2\sqrt2+3\sqrt3)(2\sqrt2-3\sqrt3)}$

We know that,

$\hookrightarrow(a+b)(a-b)=a^2-b^2$

So,

$\implies\dfrac{(2\sqrt3-\sqrt5)(2\sqrt2-3\sqrt3)}{(2\sqrt2+3\sqrt3)(2\sqrt2-3\sqrt3)}$

$\implies\dfrac{4\sqrt6-18-2\sqrt{10}+3\sqrt{15}}{(2\sqrt2)^2-(3\sqrt3)^2}$

$\implies\dfrac{4\sqrt6-18-2\sqrt{10}+3\sqrt{15}}{8-27}$

So,

$\implies\dfrac{4\sqrt6-18-2\sqrt{10}+3\sqrt{15}}{-19}$

$\implies\dfrac{-(4\sqrt6-18-2\sqrt{10}+3\sqrt{15})}{19}$

$\implies\dfrac{-4\sqrt6+18+2\sqrt{10}-3\sqrt{15}}{19}$

On rearranging,

$\bf\implies\dfrac{18-4\sqrt6+2\sqrt{10}-3\sqrt{15}}{19}$

Formula Used:

• $(a+b)(a-b)=a^2-b^2$