Question

rationalize the denominator 5-4√2÷2√5-3

Answer 1

!! Hey Mate !!

your answer is --

We have ,

[tex] \frac{5 - 4 \sqrt{2} }{2 \sqrt{5} - 3} \\ \\ = \frac{(5 - 4 \sqrt{2})(2 \sqrt{5} + 3)}{(2 \sqrt{5} - 3)(2 \sqrt{5} + 3) } \\ \\ = \frac{10 \sqrt{5} + 15 - 8 \sqrt{10} - 12 \sqrt{2} }{ {(2 \sqrt{5)} }^{2} - {3}^{2} } \\ \\

【 Hope it helps you 】

Answer 2

Hello friends!!

Here is your answer :

$\frac{5 - 4 \sqrt{2} }{2 \sqrt{5} - 3}$


$= > \frac{5 - 4 \sqrt{2} }{2 \sqrt{5} - 3} \times \frac{2 \sqrt{5} + 3 }{2 \sqrt{5} + 3 }$


$= > \frac{(5 - 4 \sqrt{2} )(2 \sqrt{5} + 3) }{(2 \sqrt{5} - 3)(2 \sqrt{5} + 3)}$


Using identity :

( a + b)( a - b) = a² – b²

$= > \frac{5(2 \sqrt{5} + 3) - 4 \sqrt{2}(2 \sqrt{5} + 3) }{ {(2 \sqrt{5} )}^{2} - {(3)}^{2} }$


$= > \frac{10 \sqrt{5} + 15 - 8 \sqrt{10} - 12 \sqrt{2} }{20 - 9}$


$= > \frac{10 \sqrt{5} + 15 - 8 \sqrt{10} - 12 \sqrt{2} }{11}$


Hope it helps you... ^_^

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