Question

rationalise the denominators of following : 6+√2/6-√2​

Answer 1

Step-by-step explanation:

We multiply and divide by the conjugate of $6 - √2$ which is $6 + √2$

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

$= > \frac{ {6}^{2} + 2(6)( \sqrt{2} ) + { (\sqrt{2} )}^{2} }{36 - 2} \\ \\ = > \frac{36 + 12 \sqrt{2} + 2 }{34}$

$= > \frac{38 + 12 \sqrt{2} }{34} \\ \\ = > \frac{19 + 6 \sqrt{2} }{17}$

The Rationalised Denominator is 17...

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