Solve frac{3sqrt{10}}{10}frac{sqrt{5}}{5}+frac{sqrt{10}}{10}frac{2sqrt{5}}{5}

$$\frac{ 3 \sqrt{ 10 } }{ 10 } \frac{ \sqrt{ 5 } }{ 5 } + \frac{ \sqrt{ 10 } }{ 10 } \frac{ 2 \sqrt{ 5 } }{ 5 }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Short Solution Steps

Multiply \frac{3\sqrt{10}}{10} times \frac{\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\sqrt{10}\sqrt{5}}{10\times 5}+\frac{\sqrt{10}}{10}\times \frac{2\sqrt{5}}{5}$$

Multiply \frac{\sqrt{10}}{10} times \frac{2\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\sqrt{10}\sqrt{5}}{10\times 5}+\frac{\sqrt{10}\times 2\sqrt{5}}{10\times 5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\sqrt{10}\sqrt{5}}{10\times 5}+\frac{\sqrt{5}\sqrt{10}}{5\times 5}$$

To add or subtract expressions, expand them to make their denominators the same. Expand 5\times 5.

$$\frac{3\sqrt{10}\sqrt{5}}{5\times 10}+\frac{\sqrt{5}\sqrt{10}}{5\times 10}$$

Since \frac{3\sqrt{10}\sqrt{5}}{5\times 10} and \frac{\sqrt{5}\sqrt{10}}{5\times 10} have the same denominator, add them by adding their numerators.

$$\frac{3\sqrt{10}\sqrt{5}+\sqrt{5}\sqrt{10}}{5\times 10}$$

Do the multiplications in 3\sqrt{10}\sqrt{5}+\sqrt{5}\sqrt{10}.

$$\frac{15\sqrt{2}+5\sqrt{2}}{5\times 10}$$

Do the calculations in 15\sqrt{2}+5\sqrt{2}.

$$\frac{20\sqrt{2}}{5\times 10}$$

Cancel out 2\times 5 in both numerator and denominator.

$$\frac{2\sqrt{2}}{5}$$