Question

rationalize the denominator 5+2√3/7+4√3

Answer 1

as if you have to rationalise the denominator have to be multiplied by changing its sign.
May my answer will be helpful for u.

Answer 2

Answer:

$\frac{5+2\sqrt3}{7+4\sqrt3}=11-6\sqrt3$

Step-by-step explanation:

Given : Expression $\frac{5+2\sqrt3}{7+4\sqrt3}$

To find : Rationalize the denominator ?

Solution :

Expression $\frac{5+2\sqrt3}{7+4\sqrt3}$

Rationalize the denominator by multiplying and dividing by denominator,

$=\frac{5+2\sqrt3}{7+4\sqrt3}\times\frac{7-4\sqrt3}{7-4\sqrt3}$

$=\frac{(5+2\sqrt3)(7-4\sqrt3)}{(7+4\sqrt3)(7-4\sqrt3)}$

$=\frac{35-20\sqrt3+14\sqrt3-8\times 3}{7^2-(4\sqrt3)^2}$

$=\frac{35-6\sqrt3-24}{49-48}$

$=\frac{11-6\sqrt3}{1}$

$=11-6\sqrt3$

Therefore, Rationalization is $\frac{5+2\sqrt3}{7+4\sqrt3}=11-6\sqrt3$