Solve sqrt{562div632}

$$\sqrt{ 562 \div 632 }$$

Evaluate

$$\frac{\sqrt{22199}}{158}\approx 0.942995496$$

Solution Steps

Reduce the fraction \frac{562}{632} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{281}{316}}$$

Rewrite the square root of the division \sqrt{\frac{281}{316}} as the division of square roots \frac{\sqrt{281}}{\sqrt{316}}.

$$\frac{\sqrt{281}}{\sqrt{316}}$$

Factor 316=2^{2}\times 79. Rewrite the square root of the product \sqrt{2^{2}\times 79} as the product of square roots \sqrt{2^{2}}\sqrt{79}. Take the square root of 2^{2}.

$$\frac{\sqrt{281}}{2\sqrt{79}}$$

Rationalize the denominator of \frac{\sqrt{281}}{2\sqrt{79}} by multiplying numerator and denominator by \sqrt{79}.

$$\frac{\sqrt{281}\sqrt{79}}{2\left(\sqrt{79}\right)^{2}}$$

The square of \sqrt{79} is 79.

$$\frac{\sqrt{281}\sqrt{79}}{2\times 79}$$

To multiply \sqrt{281} and \sqrt{79}, multiply the numbers under the square root.

$$\frac{\sqrt{22199}}{2\times 79}$$

Multiply 2 and 79 to get 158.

$$\frac{\sqrt{22199}}{158}$$