Solve sqrt{251/52}

$$\sqrt{ \frac{ 251 }{ 52 } }$$

Evaluate

$$\frac{\sqrt{3263}}{26}\approx 2.197025962$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{251}{52}} as the division of square roots \frac{\sqrt{251}}{\sqrt{52}}.

$$\frac{\sqrt{251}}{\sqrt{52}}$$

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$\frac{\sqrt{251}}{2\sqrt{13}}$$

Rationalize the denominator of \frac{\sqrt{251}}{2\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{\sqrt{251}\sqrt{13}}{2\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{\sqrt{251}\sqrt{13}}{2\times 13}$$

To multiply \sqrt{251} and \sqrt{13}, multiply the numbers under the square root.

$$\frac{\sqrt{3263}}{2\times 13}$$

Multiply 2 and 13 to get 26.

$$\frac{\sqrt{3263}}{26}$$