Question

Rationalise the denominator 1/4+√5

Answer 1

$hey \: mate \: here \: is \: your \: answer \:$

$\textbf{Given to ➡️}$. We Need To Rationalize The Denominator Of --

$\frac{1}{4 + \sqrt{5} }$

$\textbf{Solution}$

Now To Rationalize Follow Some Simple Steps...

1)) Find Rationalising Factor Of The Term ....

That is here term which is to be RATIONALIZED is

$4 + \sqrt{5}$

So Rationalising factor of this term is

$4 - \sqrt{5} \: \: (as \: rationalising \: factor \: of \: (a + b) \: is \: \: (a - b)$

So We Need To Multiply This Rationalising Factor To Both Numerator And Denominator As The Value Of Term

Should Not Be Changed .

That is ➡️

$\frac{1}{4 + \sqrt{5} } \times \frac{(4 - \sqrt{5)} }{(4 - \sqrt{5} )}$

That is ➡️

$\frac{4 - \sqrt{5} }{(4 + \sqrt{5} )(4 - \sqrt{5} }$

So Now We Know An Indentity That Is ➡️

$(a + b )\: (a - b) = {a}^{2} - {b}^{2}$

Now Applying This Identity In Denominator Where

a = 4 & b = √5

So We Have .......

$\frac{4 - \sqrt{5} }{ {(4)}^{2} - {( \sqrt{5)} }^{2} }$

That Is ➡️

$\frac{4 - \sqrt{5} }{16 - 5} \: (as \: {4}^{2} = 16 \: and \: { (\sqrt{5} )}^{2} = 5)$

So We Have Rationalized Factor As ....

$\frac{4 - \sqrt{5} }{11}$

$\textbf{Hence the answer is}$

$\frac{4 - \sqrt{5} }{11}$

$\: hope \: its \: help \: full \: .........$

$be \: brainly$

Thought Of The Day ......

"Success Is Not A Thing Which Comes In Our Life But It Is The Thing Which We Need To Follow In Our Life"

Thought made by Me ...

Answer 2

hey mate here is your answer:-

= 1/4+√5×4-√5/4-√5

= 4-√5/(4-(√5))²

= 4-√5/16-5

= 4-√5/11...

I hope it's help you....✌️