Question

1 / 8 + 5root 2 rationalise the denominator

Answer 1

Aim:-

To rationalise the denominator of  $\frac{1}{8+5\sqrt{2} }$

Procedure of solving:-

• In order to rationalise the denominator, we need to multiply the given fraction by $\frac{8-5\sqrt{2} }{8-5\sqrt{2}}$.
• After rationalising the denominator, we can find the value of the result.

Solution:-

On rationalising $\frac{1}{8+5\sqrt{2} }$,

$\frac{1}{8+5\sqrt{2} }\times\frac{8-5\sqrt{2} }{8-5\sqrt{2}}$

$=\frac{1(8-5\sqrt{2}) }{(8+5\sqrt{2})(8-5\sqrt{2} ) }$

⇒ $\frac{8-5\sqrt{2} }{(8)^2-(5\sqrt{2})^2 }$ $($∵ $(a+b)(a-b)=a^2-b^2)$

⇒ $\frac{8-5\sqrt{2} }{64-50 }$

⇒ $\frac{8-5\sqrt{2} }{14 }$

Conclusion:-

∴ $\boxed{\frac{1}{8+5\sqrt{2} }=\frac{8-5\sqrt{2} }{14}}$