Question

Rationalise the denominator of 1/8+5√2

Answer 1

Rationalizing is the process to make the denominator surd free
It means that no root remains in that.

The prescribed process of rationalizing is to multiply the number which is equal to denominator but inverse in sign, to both the Numerator and denominator.

So,
We have a number
$\frac{1}{8 + 5 \sqrt{2} } \\ = \frac{1(8 - 5 \sqrt{2} )}{(8 + 5 \sqrt{2} )(8 - 5 \sqrt{2} )} \\ \\ = \frac{8 - 5 \sqrt{2} }{( {8}^{2}) - {(5 \sqrt{2} )}^{2} } \\ using \: the \: formula \: (x + y)(x - y) \\ = {x}^{2} + {y}^{2} \\ \\ = \frac{8 - 5 \sqrt{2} }{64 - 50} \\ \\ = \frac{8 - 5 \sqrt{2} }{14} (ans)$

Answer 2

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