Question

Rationalize the Denominator 4 + √5 divided
by 4 - √5

Answer 1

$\frac{4 + \sqrt{5} }{4 - \sqrt{5} } \\ \\ \\ \mathbb{By \: \: \: Rationalization} \\ \\ \\ = > \frac{4 + \sqrt{5} }{4 - \sqrt{5} } \times \frac{4 + \sqrt{5} }{4 + \sqrt{5} } \\ \\ \\ = > \frac{ {(4 + \sqrt{5} )}^{2} }{ {4}^{2} - {( \sqrt{5}) }^{2} } \\ \\ \\ => \frac{16 + 5 + 8 \sqrt{5} }{16 - 5} \\ \\ \\ => \frac{21 + 8 \sqrt{5} }{11}$



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Answer 2

Hey

Here is your answer,

= 4 + √5 / 4-√5
= 4+√5 / 4-√5 x 4+√5 / 4+√5
= (4+√5)^2 / (4)^2 - (√5)^2

Since (4+√5)^2 is in the form of (a+b)^2 , we apply the identity
(a+b)^2 = a^2 + b^2 + 2ab and ,
(4)^2 - (√5)^2 is in the form of a^2 - b^2 , we apply the identity
a^2 - b^2 = (a+b)(a-b)

= 16+5+8√5 / 16-5
= 21+8√5/11

Hope it helps you!