Question

Vayu~

Q1.Rationalise the denominator of 5+2√3 / 7+4√3​.​

Answer 1

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

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

$@vikramjeeth$