Question

Simplify 5+ 3root /5-3root

Answer 1

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

___________ [GIVEN]

• We have to simplify it by rationalizing.

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

=> $\dfrac{5 \: + \: \sqrt{3} }{5 \: - \: \sqrt{3} } \: \times \: \dfrac{5 \: + \: \sqrt{3} }{5 \: + \: \sqrt{3} }$

• (a + b) (a + b) = a² + b² + 2ab

• (a + b) (a - b) = a² - b²

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

=> $\dfrac{ {(5)}^{2} \: + \: {( \sqrt{3} )}^{2} \: + \: 2(5)( \sqrt{3}) }{ 25 \: - \: 3 }$

=> $\dfrac{ 25 \: + \: 3 \: + \: 10\sqrt{3} }{ 22 }$

=> $\dfrac{ 28 \: + \: 10\sqrt{3} }{ 22 }$

=> $\dfrac{2( 14 \: + \: 5\sqrt{3} )}{ 2(11) }$

=> $\dfrac{ 14 \: + \: 5\sqrt{3} }{ 11}$

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$\dfrac{ 14 \: + \: 5\sqrt{3} }{ 11}$

__________ [ANSWER]

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