Question

by Rationalise the denominator 1/3 -2 root2​

Answer 1

We have,

• To rationalize $\frac{1}{3 - 2 \sqrt{2} }$

Here,

• For this purpose, we need to multiply the fraction with 3 + 2√2 so as to eradicate 2√2 from denominator.

Thus,

$\bf \frac{1}{3 - 2 \sqrt{2} } \times \frac{3 + 2 \sqrt{2}}{3 + 2 \sqrt{2}} \\ \\ \tt \frac{3 + 2 \sqrt{2} }{(3 - 2 \sqrt{2})(3 - 2 \sqrt{2})}$

• Denominator is in form (a + b)(a - b), so, identity applied will be

$\bull \: \: \rm \pink{ {a}^{2} - {b}^{2} } = \blue{(a + b)(a - b)}$

Now,

$\to \tt \frac{3 + 2 \sqrt{2} }{ {(3)}^{2} - {(2 \sqrt{2} )}^{2} } \\ \\ \to \tt \frac{3 + 2 \sqrt{2} }{9 - 8} \\ \\ \to \bf \red{ 3 + 2 \sqrt{2} }$

Hence,

• Rationalised fraction of $\sf \frac{1}{3 - 2 \sqrt{2} }$ will be $\sf 3 + 2 \sqrt{2}$