Question

Given that (√3 +√5)÷√5=x+y√15 what is the value of (x+y)?.

Answer 1

Answer:

$x+y=\frac{6}{5}$

Step-by-step explanation:

$\frac{(\sqrt{3} +\sqrt{5} )}{\sqrt{5} } =x+y\sqrt{15}$

     Multiply both the numerator and denominator of the left hand side by $\sqrt{5}$ to get,

   L.H.S.:-

                   $=\frac{(\sqrt{3} +\sqrt{5} )\cdot \sqrt{5} }{\sqrt{5} \cdot\sqrt{5} } \\ \\ =\frac{\sqrt{3} \cdot \sqrt{5}+\sqrt{5}\cdot\sqrt{5} }{\sqrt{5} \cdot\sqrt{5} } \\ \\ =\frac{\sqrt{15}+5 }{5} \\ \\ =\frac{\sqrt{15} }{5} +\frac{5}{5}$

R.H.S.:-

                  $x+y\sqrt{15}$

Comparing L.H.S and R.H.S,

                 $x=1\\ \\ y=\frac{1}{5}$

Thus,

               $x+y=1+\frac{1}{5}\\ \\ =\frac{5+1}{5}\\ \\ =\frac{6}{5}$