Question

The rationalizing factor of 7-2underoot 3

Answer 1

Answer:

The rationalizing factor of

$7 - 2 \sqrt{3} \: is \: 7 + 2 \sqrt{3}$

Answer 2

Correct Question

The rationalizing factor of $\frac{1}{7-2{\sqrt{3}}}$

Given

$\frac{1}{7-2{\sqrt{3}}}$

To find

Rationalise $\frac{1}{7-2{\sqrt{3}}}$

Solution

let understand by indicating it as a and b

$\frac{1}{a-b{\sqrt{c}}}$= $\frac{1}{a-b{\sqrt{c}}}\times\frac{a+b{\sqrt{c}}}{a+b{\sqrt{c}}}$

Now solving

$\implies\frac{1}{7-2{\sqrt{3}}}$= $\frac{1}{7-2{\sqrt{3}}}\times\frac{7+2{\sqrt{3}}}{7+2{\sqrt{3}}}$

$\implies\frac{1}{7-2{\sqrt{3}}}$= $\frac{7+2{\sqrt{3}}}{37}$

Hence,

$\implies\frac{1}{7-2{\sqrt{3}}}$= $\frac{7+2{\sqrt{3}}}{37}$