Question

this is from square roots chapter
pls help me simplify

Answer 1

Given:-

• $\dfrac{ \sqrt{31.36 } + \sqrt{6.76} }{\sqrt{31.36 } - \sqrt{6.76}}$

Solution:-

$\frac{ \sqrt{31.36 } + \sqrt{6.76} }{\sqrt{31.36 } - \sqrt{6.76}}$

Rationalising by dividing denominator as well as numerator by (√31.36 +√6.76)

$\implies \: \frac{ (\sqrt{31.36 } + \sqrt{6.76}) (\sqrt{31.36 } + \sqrt{6.76})}{(\sqrt{31.36 } - \sqrt{6.76})(\sqrt{31.36 } + \sqrt{6.76})}$

$\implies \: \frac{ (\sqrt{31.36 } + \sqrt{6.76})^{2} }{(\sqrt{31.36 }) ^{2} - (\sqrt{6.76}) ^{2} }$

$\implies \: \frac{ 31.36 + 6.76 + 2( \sqrt{31.36} )( \sqrt{6.76} )}{24.5}$

$\implies \: \frac{ 31.36 + 6.76 + 2(5.6)(2.6)}{24.5}$

$\implies \: \frac{ 31.36 + 6.76 + 29.12}{24.5}$

$\implies \: \frac{ 67.24}{24.5}$

$\implies \: 2.75(approx)$