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\frac{\sqrt{10}\sqrt{5}}{10\times 5}+\frac{3\sqrt{10}}{10}\times \frac{2\sqrt{5}}{5}
Multiply \frac{\sqrt{10}}{10} times \frac{\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.
\frac{\sqrt{10}\sqrt{5}}{10\times 5}+\frac{3\sqrt{10}\times 2\sqrt{5}}{10\times 5}
Multiply \frac{3\sqrt{10}}{10} times \frac{2\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.
\frac{\sqrt{10}\sqrt{5}}{10\times 5}+\frac{3\sqrt{5}\sqrt{10}}{5\times 5}
Cancel out 2 in both numerator and denominator.
\frac{\sqrt{10}\sqrt{5}}{5\times 10}+\frac{3\sqrt{5}\sqrt{10}}{5\times 10}
To add or subtract expressions, expand them to make their denominators the same. Expand 5\times 5.
\frac{\sqrt{10}\sqrt{5}+3\sqrt{5}\sqrt{10}}{5\times 10}
Since \frac{\sqrt{10}\sqrt{5}}{5\times 10} and \frac{3\sqrt{5}\sqrt{10}}{5\times 10} have the same denominator, add them by adding their numerators.
\frac{5\sqrt{2}+15\sqrt{2}}{5\times 10}
Do the multiplications in \sqrt{10}\sqrt{5}+3\sqrt{5}\sqrt{10}.
\frac{20\sqrt{2}}{5\times 10}
Do the calculations in 5\sqrt{2}+15\sqrt{2}.
\frac{2\sqrt{2}}{5}
Cancel out 2\times 5 in both numerator and denominator.