Solve sqrt{249*896/3,14*7}

$$\sqrt { \frac { 249 \cdot 896 } { 3,14 \times 7 } }$$

Evaluate

$$\frac{80\sqrt{39093}}{157}\approx 100.748788932$$

Solution Steps

Cancel out 7 in both numerator and denominator.

$$\sqrt{\frac{128\times 249}{3,14}}$$

Multiply 128 and 249 to get 31872.

$$\sqrt{\frac{31872}{3,14}}$$

Expand \frac{31872}{3,14} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{3187200}{314}}$$

Reduce the fraction \frac{3187200}{314} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{1593600}{157}}$$

Rewrite the square root of the division \sqrt{\frac{1593600}{157}} as the division of square roots \frac{\sqrt{1593600}}{\sqrt{157}}.

$$\frac{\sqrt{1593600}}{\sqrt{157}}$$

Factor 1593600=80^{2}\times 249. Rewrite the square root of the product \sqrt{80^{2}\times 249} as the product of square roots \sqrt{80^{2}}\sqrt{249}. Take the square root of 80^{2}.

$$\frac{80\sqrt{249}}{\sqrt{157}}$$

Rationalize the denominator of \frac{80\sqrt{249}}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{80\sqrt{249}\sqrt{157}}{\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{80\sqrt{249}\sqrt{157}}{157}$$

To multiply \sqrt{249} and \sqrt{157}, multiply the numbers under the square root.

$$\frac{80\sqrt{39093}}{157}$$