Solve sqrt{1122/315}

$$\sqrt{ \frac{ 1122 }{ 315 } }$$

Evaluate

$$\frac{\sqrt{39270}}{105}\approx 1.88730092$$

Solution Steps

Reduce the fraction \frac{1122}{315} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{374}{105}}$$

Rewrite the square root of the division \sqrt{\frac{374}{105}} as the division of square roots \frac{\sqrt{374}}{\sqrt{105}}.

$$\frac{\sqrt{374}}{\sqrt{105}}$$

Rationalize the denominator of \frac{\sqrt{374}}{\sqrt{105}} by multiplying numerator and denominator by \sqrt{105}.

$$\frac{\sqrt{374}\sqrt{105}}{\left(\sqrt{105}\right)^{2}}$$

The square of \sqrt{105} is 105.

$$\frac{\sqrt{374}\sqrt{105}}{105}$$

To multiply \sqrt{374} and \sqrt{105}, multiply the numbers under the square root.

$$\frac{\sqrt{39270}}{105}$$