Question

Retionalize the denominator 3 by 2+√3​

Answer 1

Answer:

To rationalise the denominator, multiply the numerator and denominator by the rationalising factor i.e.(2 + √3)

Hope this helps you☺

Answer 2

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Rationalize the denominator 3 by 2+√3

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• Rationalising means Multiply the numerator and denominator by rationalising factor with its opposite sign if sign is positive then multiply numerator and denominator with negative sign and vice -versa.

$= > \frac{3}{2 + \sqrt{3} }$

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

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

Here ,this identity is used:

$\bold{\boxed{{\red{(x + y)(x - y) }}= {x}^{2} - {y}^{2}}}$

$= > \frac{6 - 3 \sqrt{3} }{ {(2)}^{2} - {( \sqrt{3}) }^{2} }$

$= > \frac{6 - 3 \sqrt{3} }{4 - 3}$

$\bold{= 6 - 3 \sqrt{3} }✓$

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