Solve frac{sqrt{5}}{5}*(-frac{7sqrt{2}}{10})+frac{2sqrt{5}}{5}*(frac{sqrt{2}}{10})

$$\frac { \sqrt { 5 } } { 5 } \times ( - \frac { 7 \sqrt { 2 } } { 10 } ) + \frac { 2 \sqrt { 5 } } { 5 } \times ( \frac { \sqrt { 2 } } { 10 } )$$

Evaluate

$$-\frac{\sqrt{10}}{10}\approx -0.316227766$$

Short Solution Steps

Multiply \frac{\sqrt{5}}{5} times -\frac{7\sqrt{2}}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\sqrt{5}\times 7\sqrt{2}}{5\times 10}+\frac{2\sqrt{5}}{5}\times \frac{\sqrt{2}}{10}$$

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

$$\frac{-\sqrt{5}\times 7\sqrt{2}}{5\times 10}+\frac{2\sqrt{5}\sqrt{2}}{5\times 10}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-\sqrt{5}\times 7\sqrt{2}}{5\times 10}+\frac{\sqrt{2}\sqrt{5}}{5\times 5}$$

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

$$\frac{-\sqrt{5}\times 7\sqrt{2}}{5\times 10}+\frac{\sqrt{2}\sqrt{5}}{5\times 10}$$

Since \frac{-\sqrt{5}\times 7\sqrt{2}}{5\times 10} and \frac{\sqrt{2}\sqrt{5}}{5\times 10} have the same denominator, add them by adding their numerators.

$$\frac{-\sqrt{5}\times 7\sqrt{2}+\sqrt{2}\sqrt{5}}{5\times 10}$$

Do the multiplications in -\sqrt{5}\times 7\sqrt{2}+\sqrt{2}\sqrt{5}.

$$\frac{-7\sqrt{10}+\sqrt{10}}{5\times 10}$$

Do the calculations in -7\sqrt{10}+\sqrt{10}.

$$\frac{-6\sqrt{10}}{5\times 10}$$

Cancel out 2 in both numerator and denominator.

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

Expand 5\times 5.

$$\frac{-3\sqrt{10}}{25}$$