Solve sqrt{1181/156}

$$\sqrt { \frac { 1181 } { 156 } }$$

Evaluate

$$\frac{\sqrt{46059}}{78}\approx 2.751456491$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1181}{156}} as the division of square roots \frac{\sqrt{1181}}{\sqrt{156}}.

$$\frac{\sqrt{1181}}{\sqrt{156}}$$

Factor 156=2^{2}\times 39. Rewrite the square root of the product \sqrt{2^{2}\times 39} as the product of square roots \sqrt{2^{2}}\sqrt{39}. Take the square root of 2^{2}.

$$\frac{\sqrt{1181}}{2\sqrt{39}}$$

Rationalize the denominator of \frac{\sqrt{1181}}{2\sqrt{39}} by multiplying numerator and denominator by \sqrt{39}.

$$\frac{\sqrt{1181}\sqrt{39}}{2\left(\sqrt{39}\right)^{2}}$$

The square of \sqrt{39} is 39.

$$\frac{\sqrt{1181}\sqrt{39}}{2\times 39}$$

To multiply \sqrt{1181} and \sqrt{39}, multiply the numbers under the square root.

$$\frac{\sqrt{46059}}{2\times 39}$$

Multiply 2 and 39 to get 78.

$$\frac{\sqrt{46059}}{78}$$