Solve sqrt{100div3.14}

$$\sqrt{ 100 \div 3.14 }$$

Evaluate

$$\frac{50\sqrt{314}}{157}\approx 5.64332648$$

Solution Steps

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

$$\sqrt{\frac{10000}{314}}$$

Reduce the fraction \frac{10000}{314} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{5000}{157}}$$

Rewrite the square root of the division \sqrt{\frac{5000}{157}} as the division of square roots \frac{\sqrt{5000}}{\sqrt{157}}.

$$\frac{\sqrt{5000}}{\sqrt{157}}$$

Factor 5000=50^{2}\times 2. Rewrite the square root of the product \sqrt{50^{2}\times 2} as the product of square roots \sqrt{50^{2}}\sqrt{2}. Take the square root of 50^{2}.

$$\frac{50\sqrt{2}}{\sqrt{157}}$$

Rationalize the denominator of \frac{50\sqrt{2}}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{50\sqrt{2}\sqrt{157}}{\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{50\sqrt{2}\sqrt{157}}{157}$$

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

$$\frac{50\sqrt{314}}{157}$$