Solve sqrt{26*36/3.14}

$$\sqrt { \frac { 26 \times 36 } { 3.14 } }$$

Evaluate

$$\frac{60\sqrt{2041}}{157}\approx 17.265259105$$

Solution Steps

Multiply 26 and 36 to get 936.

$$\sqrt{\frac{936}{3.14}}$$

Expand \frac{936}{3.14} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{93600}{314}}$$

Reduce the fraction \frac{93600}{314} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{46800}{157}}$$

Rewrite the square root of the division \sqrt{\frac{46800}{157}} as the division of square roots \frac{\sqrt{46800}}{\sqrt{157}}.

$$\frac{\sqrt{46800}}{\sqrt{157}}$$

Factor 46800=60^{2}\times 13. Rewrite the square root of the product \sqrt{60^{2}\times 13} as the product of square roots \sqrt{60^{2}}\sqrt{13}. Take the square root of 60^{2}.

$$\frac{60\sqrt{13}}{\sqrt{157}}$$

Rationalize the denominator of \frac{60\sqrt{13}}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{60\sqrt{13}\sqrt{157}}{\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{60\sqrt{13}\sqrt{157}}{157}$$

To multiply \sqrt{13} and \sqrt{157}, multiply the numbers under the square root.

$$\frac{60\sqrt{2041}}{157}$$