1.

1 / 8 + 5root 2 rationalise the denominator

Answer»

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}}


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