Solve sqrt{900/62}

$$\sqrt{ \frac{ 900 }{ 62 } }$$

Evaluate

$$\frac{15\sqrt{62}}{31}\approx 3.81000381$$

Solution Steps

Reduce the fraction \frac{900}{62} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{450}{31}}$$

Rewrite the square root of the division \sqrt{\frac{450}{31}} as the division of square roots \frac{\sqrt{450}}{\sqrt{31}}.

$$\frac{\sqrt{450}}{\sqrt{31}}$$

Factor 450=15^{2}\times 2. Rewrite the square root of the product \sqrt{15^{2}\times 2} as the product of square roots \sqrt{15^{2}}\sqrt{2}. Take the square root of 15^{2}.

$$\frac{15\sqrt{2}}{\sqrt{31}}$$

Rationalize the denominator of \frac{15\sqrt{2}}{\sqrt{31}} by multiplying numerator and denominator by \sqrt{31}.

$$\frac{15\sqrt{2}\sqrt{31}}{\left(\sqrt{31}\right)^{2}}$$

The square of \sqrt{31} is 31.

$$\frac{15\sqrt{2}\sqrt{31}}{31}$$

To multiply \sqrt{2} and \sqrt{31}, multiply the numbers under the square root.

$$\frac{15\sqrt{62}}{31}$$