Solve frac{3sqrt{10}}{10}*frac{sqrt{5}}{5}+frac{sqrt{10}}{10}*frac{2sqrt{15}}{5}

$$\frac { 3 \sqrt { 10 } } { 10 } \times \frac { \sqrt { 5 } } { 5 } + \frac { \sqrt { 10 } } { 10 } \times \frac { 2 \sqrt { 15 } } { 5 }$$

Evaluate

$$\frac{\sqrt{2}\left(2\sqrt{3}+3\right)}{10}\approx 0.914162017$$

Short Solution Steps

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

$$\frac{3\sqrt{10}\sqrt{5}}{10\times 5}+\frac{\sqrt{10}}{10}\times \frac{2\sqrt{15}}{5}$$

Multiply \frac{\sqrt{10}}{10} times \frac{2\sqrt{15}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\sqrt{10}\sqrt{5}}{10\times 5}+\frac{\sqrt{10}\times 2\sqrt{15}}{10\times 5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\sqrt{10}\sqrt{5}}{10\times 5}+\frac{\sqrt{10}\sqrt{15}}{5\times 5}$$

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

$$\frac{3\sqrt{10}\sqrt{5}}{5\times 10}+\frac{\sqrt{10}\sqrt{15}}{5\times 10}$$

Since \frac{3\sqrt{10}\sqrt{5}}{5\times 10} and \frac{\sqrt{10}\sqrt{15}}{5\times 10} have the same denominator, add them by adding their numerators.

$$\frac{3\sqrt{10}\sqrt{5}+\sqrt{10}\sqrt{15}}{5\times 10}$$

Do the multiplications in 3\sqrt{10}\sqrt{5}+\sqrt{10}\sqrt{15}.

$$\frac{15\sqrt{2}+5\sqrt{6}}{5\times 10}$$

Expand 5\times 10.

$$\frac{15\sqrt{2}+5\sqrt{6}}{50}$$

Factor

$$\frac{\sqrt{2} {(\sqrt{2} \sqrt{6} + 3)}}{10} = 0.9141620172685642$$