Question

rationalise the denominator of 1/√7-2

Answer 1

1/✓7-2*√7+2/√7+2=√7+2/(√7)^2-(2)^2
=√7+2/7-4
=√7+2/3

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

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

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

$= \frac{1( \sqrt{7} + 2) }{( \sqrt{7} - 2)( \sqrt{7} + 2) }$

$= \frac{ \sqrt{7} + 2}{( \sqrt{7} {)}^{2} - ( 2 {)}^{2} }$

$= \frac{ \sqrt{7} + 2 }{7 - 4}$

$= \frac{ \sqrt{7} + 2}{3}$

$\bf{Hence \: the \: denominator \: is \: rationalised.}$