Solve 3/5*frac{sqrt{2}}{2}+4/5*frac{sqrt{2}}{2}

$$\frac { 3 } { 5 } \times \frac { \sqrt { 2 } } { 2 } + \frac { 4 } { 5 } \times \frac { \sqrt { 2 } } { 2 }$$

Evaluate

$$\frac{7\sqrt{2}}{10}\approx 0.989949494$$

Short Solution Steps

Multiply \frac{3}{5} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\sqrt{2}}{5\times 2}+\frac{4}{5}\times \frac{\sqrt{2}}{2}$$

Multiply \frac{4}{5} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\sqrt{2}}{5\times 2}+\frac{4\sqrt{2}}{5\times 2}$$

Cancel out 2 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\times 2 and 5 is 2\times 5. Multiply \frac{2\sqrt{2}}{5} times \frac{2}{2}.

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

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

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

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

$$\frac{3\sqrt{2}+4\sqrt{2}}{2\times 5}$$

Do the calculations in 3\sqrt{2}+4\sqrt{2}.

$$\frac{7\sqrt{2}}{2\times 5}$$

Expand 2\times 5.

$$\frac{7\sqrt{2}}{10}$$