Simplifying Radical Expressions| Algebra| ENGG10 LE2 Problem 3

Reduce to a simple fraction in lowest term.

\frac{x^{\frac{3}{2}}+y^{\frac{3}{2}}}{\sqrt{x}+\sqrt{y}}

SOLUTION:

\frac{x^{\frac{3}{2}}+y^{\frac{3}{2}}}{\sqrt{x}+\sqrt{y}}

=\frac{\left(\sqrt{x}\right)^3+\left(\sqrt{y}\right)^3}{\sqrt{x}+\sqrt{y}}

=\frac{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x^2}-\sqrt{xy}+\sqrt{y^2}\right)}{\sqrt{x}+\sqrt{y}}

=x-\sqrt{xy}+y