Question

Rationalise 2- 3 root3 / 2+3root3

Answer 1

Hey Mate!
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Here is your answer :

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Given,

$\frac{2 - 3 \sqrt{3} }{2 + 3 \sqrt{3} }$

Rationalise the Denominator.

$\frac{2 - 3 \sqrt{3} }{2 + 3 \sqrt{3} } = \frac{2 - 3 \sqrt{3} }{2 + 3 \sqrt{3} } \times \frac{ 2 - 3 \sqrt{3} }{2 + 3 \sqrt{3} } \\ \\ = \frac{2(3 - 3 \sqrt{3)} - 3 \sqrt{3} (2 - 3 \sqrt{3}) }{(a + b)(a - b)} \\ \\ = \frac{6 - 6 \sqrt{3} - 6 \sqrt{3} + 6 \sqrt{3} }{ {a}^{2} - {b}^{2} } \\ \\ = \frac{6 - 6 \sqrt{3} }{ {2}^{2} - {(3 \sqrt{3)} }^{2} } \\ \\ = \frac{ \sqrt{3} }{4 - 27} \\ \\ = \frac{ \sqrt{3} }{4 - 27} \\ \\ = \frac{ \sqrt{3} }{ - 23}$

HOPE THIS HELPS U...

Answer 2

Hey !!

Here's your answer.. ⬇⬇

$= \frac{2 - 3 \sqrt{3} }{2 + 3 \sqrt{3} } \\ \\ multiply \: \: numerator \: \: and \: \: denominator \: \: by \: \: 2 - 3 \sqrt{3} \\ \\ = \frac{2 - 3 \sqrt{3} }{2 + 3 \sqrt{3} } \times \frac{2 - 3 \sqrt{3} }{2 - 3 \sqrt{3} } \\ \\ = \frac{ ({2 - 3 \sqrt{3}) }^{2} }{( 2 + 3 \sqrt{3})(2 - 3 \sqrt{3} )} \\ \\ = \frac{ {2}^{2} - 2(2)(3 \sqrt{3} ) + ({3 \sqrt{3}) }^{2} }{ ({2}^{2} ) - {(3 \sqrt{3}) }^{2} } \\ \\ = \frac{4 - 12 \sqrt{3} + 27}{4 - 27} \\ \\ = \frac{31 - 12 \sqrt{3} }{ - 23}$


HOPE IT HELPS..

THANKS ^-^