Solve sqrt{100div314}

$$\sqrt{ 100 \div 314 }$$

Evaluate

$$\frac{5\sqrt{314}}{157}\approx 0.564332648$$

Solution Steps

Reduce the fraction \frac{100}{314} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{50}{157}}$$

Rewrite the square root of the division \sqrt{\frac{50}{157}} as the division of square roots \frac{\sqrt{50}}{\sqrt{157}}.

$$\frac{\sqrt{50}}{\sqrt{157}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{5\sqrt{2}}{\sqrt{157}}$$

Rationalize the denominator of \frac{5\sqrt{2}}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{5\sqrt{2}\sqrt{157}}{\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{5\sqrt{2}\sqrt{157}}{157}$$

To multiply \sqrt{2} and \sqrt{157}, multiply the numbers under the square root.

$$\frac{5\sqrt{314}}{157}$$