Question

rationalise the denominator 1/√3-√7​

Answer 1

Answer:

1/√3-√7

=1(√3+√7) /(√3-√7) (√3+√7)

=√3+√7/3-7

=√3+√7/-4

Answer 2

$\huge\sf{\bold\purple{Question \: – } }$

Rationalise the denominator -

• $\frac{1}{ \sqrt{3} - \sqrt{7} }$

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✯ By 'rationalising the denominator' here, it is meant that we just have to change the irrational denominator into a rational one.

✯In such problems, we just need to multiply both the numerator and the denominator with the opposite sign of denominator.

Let's rationalise the given real number –

$\frac{1}{ \sqrt{3} - \sqrt{7} } \\ \\ \implies \frac{1}{ \sqrt{3} - \sqrt{7} } \times \frac{ \sqrt{3} + \sqrt{7} }{ \sqrt{3} + \sqrt{7} } \\ \\ \implies \frac{ \sqrt{3} + \sqrt{7} }{3 - 7} \\ \\ \implies \: \boxed{\frac{ \sqrt{3} + \sqrt{7} }{ - 4} }$

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Therefore,

$\frac{1}{ \sqrt{3} - \sqrt{7} } = \frac{ \sqrt{3} + \sqrt{7} }{ - 4}$

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⠀⠀✨ HOPE IT HELPS✨