Solve sqrt{115/41}

$$\sqrt { 1 \frac { 15 } { 41 } }$$

Evaluate

$$\frac{2\sqrt{574}}{41}\approx 1.16869742$$

Solution Steps

Multiply 1 and 41 to get 41.

$$\sqrt{\frac{41+15}{41}}$$

Add 41 and 15 to get 56.

$$\sqrt{\frac{56}{41}}$$

Rewrite the square root of the division \sqrt{\frac{56}{41}} as the division of square roots \frac{\sqrt{56}}{\sqrt{41}}.

$$\frac{\sqrt{56}}{\sqrt{41}}$$

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$\frac{2\sqrt{14}}{\sqrt{41}}$$

Rationalize the denominator of \frac{2\sqrt{14}}{\sqrt{41}} by multiplying numerator and denominator by \sqrt{41}.

$$\frac{2\sqrt{14}\sqrt{41}}{\left(\sqrt{41}\right)^{2}}$$

The square of \sqrt{41} is 41.

$$\frac{2\sqrt{14}\sqrt{41}}{41}$$

To multiply \sqrt{14} and \sqrt{41}, multiply the numbers under the square root.

$$\frac{2\sqrt{574}}{41}$$