Question

rationalise 3+2√5 / 5-2√3 ​

Answer 1

ANSWER:

To Rationalise:

• (3 + 2√5)/(5 - 2√3)

Solution:

We are given that,

$\implies\dfrac{3+2\sqrt5}{5-2\sqrt3}$

As the denominator is 5 - 2√3, the rationalising factor will be 5 + 2√3.

So, multiplying and dividing by 5 + 2√3.

$\implies\dfrac{3+2\sqrt5}{5-2\sqrt3}\times\dfrac{5+2\sqrt3}{5+2\sqrt3}$

So,

$\implies\dfrac{(3+2\sqrt5)(5+2\sqrt3)}{(5-2\sqrt3)(5+2\sqrt3)}$

We know that,

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

So,

$\implies\dfrac{(3+2\sqrt5)(5+2\sqrt3)}{(5-2\sqrt3)(5+2\sqrt3)}$

$\implies\dfrac{(3+2\sqrt5)(5+2\sqrt3)}{(5)^2-(2\sqrt3)^2}$

On simplifying,

$\implies\dfrac{15+6\sqrt3+10\sqrt5+4\sqrt{15}}{25-12}$

Hence,

$\implies\bf\dfrac{15+6\sqrt3+10\sqrt5+4\sqrt{15}}{13}$