Solve 7/2*frac{5{2}}+25/sqrt{2}

$$\frac{ 7 }{ 2 \times \frac{ 5 }{ 2 } } + \frac{ 25 }{ \sqrt{ 2 } }$$

Evaluate

$$\frac{25\sqrt{2}}{2}+\frac{7}{5}\approx 19.07766953$$

Short Solution Steps

Cancel out 2 and 2.

$$\frac{7}{5}+\frac{25}{\sqrt{2}}$$

Rationalize the denominator of \frac{25}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{7}{5}+\frac{25\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{7}{5}+\frac{25\sqrt{2}}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2 is 10. Multiply \frac{7}{5} times \frac{2}{2}. Multiply \frac{25\sqrt{2}}{2} times \frac{5}{5}.

$$\frac{7\times 2}{10}+\frac{5\times 25\sqrt{2}}{10}$$

Since \frac{7\times 2}{10} and \frac{5\times 25\sqrt{2}}{10} have the same denominator, add them by adding their numerators.

$$\frac{7\times 2+5\times 25\sqrt{2}}{10}$$

Do the multiplications in 7\times 2+5\times 25\sqrt{2}.

$$\frac{14+125\sqrt{2}}{10}$$

Factor

$$\frac{125 \sqrt{2} + 14}{10} = 19.077669529663687$$