Question

rationalise the denominator 1 /√5-2

Answer 1

Heya !!

=1/√5-2 rationalise it
= 1/√5-2×√5+2/√5+2
=√5+2/(√5)^2-(2)^2
=√5+2/5-4
=√5+2 ..

Hope this helps you ☺

Answer 2

$\displaystyle \sf{ \frac{1 }{ \sqrt{5} - 2 } } = \sqrt{5}+2$

Given :

$\displaystyle \sf{ \frac{1 }{ \sqrt{5} - 2 } }$

To find :

To rationalize the denominator

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf{ \frac{1 }{ \sqrt{5} - 2 } }$

Step 2 of 2 :

Rationalize the denominator

$\displaystyle \sf{ \frac{1 }{ \sqrt{5} - 2 } }$

Multiplying both of the numerator and denominator by √5 + 2 we get

$\displaystyle \sf{ \frac{1 }{ \sqrt{5} - 2 } }$

$\displaystyle \sf{ = \frac{1 \times ( \sqrt{5} + 2)}{ (\sqrt{5} - 2)(\sqrt{5} + 2 ) } }$

$\displaystyle \sf{ = \frac{ (\sqrt{5} + 2 ) }{ {(\sqrt{5} )}^{2} - {( 2 )}^{2} } }$

$\displaystyle \sf{ = \frac{(\sqrt{5} + 2 ) }{ 5 - 4} }$

$\displaystyle \sf{ = \frac{ \sqrt{5} + 2 }{1} }$

$\displaystyle \sf{ = \sqrt{5} + 2 }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ the value of (√5+√2)²

https://brainly.in/question/3299659

2. Simplify ( 8+√5)(8-√5).

https://brainly.in/question/17061574

#SPJ3