Question

rationlize the denominatorof 5 + root 3 upon 7-4 root 3​

Answer 1

Hi there !!

Multiply denominator and numerator by its conjugate.

Look at the attachment ↑↑

Thankyou :)

Answer 2

$\dfrac{5 \: + \: \sqrt{3} }{7 \: - \: 4 \sqrt{3} }$

__________ [GIVEN EQUATION]

• We have to rationalize it's denominator.

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$\dfrac{5 \: + \: \sqrt{3} }{7 \: - \: 4 \sqrt{3} }$

=> $\dfrac{5 \: + \: \sqrt{3} }{7 \: - \: 4 \sqrt{3} }$ × $\dfrac{7 \: + \: 4 \sqrt{3} }{7 \: + \: 4 \sqrt{3} }$

(a - b) (a + b) = a² - b²

=> $\dfrac{(5 \: + \: 4 \sqrt{3} )(7 \: + \: 4 \sqrt{3} )}{ {(7)}^{2} \: - \: {(4 \sqrt{3} )}^{2} }$

=> $\dfrac{35 \: + \: 20 \sqrt{3} \: + \: 7 \sqrt{3} \: + \: 4( \sqrt{3}) (\sqrt{3} ) }{49 \: - \: 48}$

=> $\dfrac{35 \: + \: 27 \sqrt{3} \: + \: 12 }{1}$

=> $47\:+27\sqrt{3}$

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$\bold{47\:+27\sqrt{3}}$

___________ $\bold{[ANSWER]}$

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