Question

state true or false

Rationalisation of 1/✓6-✓3 is ✓6+✓3/2
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Answer 1

Answer:

False.

Step-by-step explanation:

$\frac{1}{ \sqrt{6 - \sqrt{3} } } \times \frac{ \sqrt{6 + \sqrt{3} } }{ \sqrt{6 + \sqrt{3} } } \\ \\ = \frac{ \sqrt{6 + \sqrt{3} } }{ { \sqrt{6} }^{2} - { \sqrt{3} }^{2} } \\ \\ = \frac{ \sqrt{6 + \sqrt{3} } }{6 - 3} \\ \\ = \frac{ \sqrt{6 + \sqrt{3} } }{3}$

Answer 2

Step-by-step explanation:

Let's check it

$\frac{1}{ \sqrt{6} - \sqrt{3} } \times \frac{ \sqrt{6} + \sqrt{3} }{ \sqrt{6} + \sqrt{3} } \\ \\ = \geqslant \frac{ \sqrt{6} + \sqrt{3} }{( \sqrt{6}) {}^{2} - (\sqrt{3} ) {}^{2} } \\ \\ = \geqslant \frac{ \sqrt{6} + \sqrt{3} }{6 - 3} \\ \\ = \geqslant \frac{ \sqrt{6} + \sqrt{3} }{3}$

So it is false