Question

8/✓3+✓5 pls rationalize the denominator​

Answer 1

Answer:

1/(8+3v5)

= 1/(8+3V5) x (8-3v5)/(8-3v5)

= (8-3v5)/(8)²-(3V5)? %3D

= (8-3v5)/(64-45) %3D

= (8-3v5)/19

Step-by-step explanation:

= (1/(8 + 3V5) }x{ (8 - 3v5)/ (8 - 3v5) } (8 - 3V5) / (8 + 3V5) (8 - 3V5)

using (a + b)(a - b)

= a? - b?

a = 8

b = 3V5

= (8 - 3V5) / (82 -(3V5)?) (8 - 3V5) / (64 - 45) = (8 - 3v5) /19 1/(8 + 3v5) = (8 - 3V5) /19

Answer 2

Answer:

$\huge \red{ \bold{ratonalizing \: the \: denominator}} \\ \frac{8}{ \sqrt{3} + \sqrt{5} } \times \frac{ \sqrt{3} - \sqrt{5} }{ \sqrt{3} - \sqrt{5} } = \frac{8( \sqrt{3} - \sqrt{5} )}{ {(\sqrt{3})}^{2} - { (\sqrt{5} )}^{2} } = \frac{8 \sqrt{3} - 8 \sqrt{5} }{3 - 5} = \frac{8 \sqrt{3} - 8 \sqrt{5} }{ - 2} \\ = \frac{8( \sqrt{3} - \sqrt{5}) }{ - 2} = - 4( \sqrt{3} - \sqrt{5} )$

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