Solve sqrt{2(169+25)-14/4}

$$\sqrt { \frac { 2 ( 169 + 25 ) - 14 } { 4 } }$$

Evaluate

$$\frac{\sqrt{374}}{2}\approx 9.669539803$$

Solution Steps

Add 169 and 25 to get 194.

$$\sqrt{\frac{2\times 194-14}{4}}$$

Multiply 2 and 194 to get 388.

$$\sqrt{\frac{388-14}{4}}$$

Subtract 14 from 388 to get 374.

$$\sqrt{\frac{374}{4}}$$

Reduce the fraction \frac{374}{4} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{187}{2}}$$

Rewrite the square root of the division \sqrt{\frac{187}{2}} as the division of square roots \frac{\sqrt{187}}{\sqrt{2}}.

$$\frac{\sqrt{187}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{187}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{187}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{187}\sqrt{2}}{2}$$

To multiply \sqrt{187} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{374}}{2}$$