Question

rationaise the following 7/√12-√5
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Answer 1

Answer:

7/√12-√5 rationalise

= 7/√12-√5×√12+√5/√12+√5

= 7(√12+√5)/√12^2-√5^2

= 7(√12+√5)/12-5

= 7(√12+√5)/7

=√12+√5 ans

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Answer 2

Rationalising the denominator

$\frac{7}{ \sqrt{12 - \sqrt{5} } }$

$= \frac{7( \sqrt{12 + \sqrt{5} } }{ \sqrt{12 - \sqrt{5} } }$

$= \frac{7 \sqrt{12 + 7 \sqrt{5} } }{ { \sqrt{12} }^{2} - { \sqrt{2} }^{2} }$

$= \frac{7 \sqrt{12 + 7 \sqrt{5} } }{12 - 5} \\ = \frac{7 \sqrt{12 + 7 \sqrt{5} } }{7}$

Taking 7 as common we get

$= \frac{7( \sqrt{12 + \sqrt{5} } }{7} ) \\ = \sqrt{12} + \sqrt{5}$