Solve frac{sqrt{5}}{5}*(-3/10sqrt{10})+(-frac{sqrt{10}}{10})*(-4/5sqrt{5})

$$\frac { \sqrt { 5 } } { 5 } \times ( - \frac { 3 } { 10 } \sqrt { 10 } ) + ( - \frac { \sqrt { 10 } } { 10 } ) \times ( - \frac { 4 } { 5 } \sqrt { 5 } )$$

Evaluate

$$\frac{\sqrt{2}}{10}\approx 0.141421356$$

Short Solution Steps

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

$$\frac{-\sqrt{5}\times 3}{5\times 10}\sqrt{10}+\left(-\frac{\sqrt{10}}{10}\right)\left(-\frac{4}{5}\right)\sqrt{5}$$

Express \frac{-\sqrt{5}\times 3}{5\times 10}\sqrt{10} as a single fraction.

$$\frac{-\sqrt{5}\times 3\sqrt{10}}{5\times 10}+\left(-\frac{\sqrt{10}}{10}\right)\left(-\frac{4}{5}\right)\sqrt{5}$$

Multiply -\frac{\sqrt{10}}{10} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\sqrt{5}\times 3\sqrt{10}}{5\times 10}+\frac{\sqrt{10}\times 4}{10\times 5}\sqrt{5}$$

Cancel out 2 in both numerator and denominator.

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

Express \frac{2\sqrt{10}}{5\times 5}\sqrt{5} as a single fraction.

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

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

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

Since \frac{-\sqrt{5}\times 3\sqrt{10}}{5\times 10} and \frac{2\sqrt{10}\sqrt{5}}{5\times 10} have the same denominator, add them by adding their numerators.

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

Do the multiplications in -\sqrt{5}\times 3\sqrt{10}+2\sqrt{10}\sqrt{5}.

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

Do the calculations in -15\sqrt{2}+10\sqrt{2}.

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

Cancel out 5 in both numerator and denominator.

$$\frac{-\sqrt{2}}{10}$$