Solve frac{frac{sqrt{2}}{2}+3^2}{21}

$$\frac { \frac { \sqrt { 2 } } { 2 } + 3 ^ { 2 } } { 21 }$$

Evaluate

$$\frac{\sqrt{2}}{42}+\frac{3}{7}\approx 0.46224318$$

Short Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{\sqrt{2}}{2}+9}{21}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{2}{2}.

$$\frac{\frac{\sqrt{2}}{2}+\frac{9\times 2}{2}}{21}$$

Since \frac{\sqrt{2}}{2} and \frac{9\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\sqrt{2}+9\times 2}{2}}{21}$$

Do the multiplications in \sqrt{2}+9\times 2.

$$\frac{\frac{\sqrt{2}+18}{2}}{21}$$

Express \frac{\frac{\sqrt{2}+18}{2}}{21} as a single fraction.

$$\frac{\sqrt{2}+18}{2\times 21}$$

Multiply 2 and 21 to get 42.

$$\frac{\sqrt{2}+18}{42}$$

Factor

$$\frac{\sqrt{2} + 18}{42} = 0.4622431800565023$$