Solve sqrt{5962/65+879}

$$\sqrt{ \frac{ 5962 }{ 65+879 } }$$

Evaluate

$$\frac{\sqrt{351758}}{236}\approx 2.513101265$$

Solution Steps

Add 65 and 879 to get 944.

$$\sqrt{\frac{5962}{944}}$$

Reduce the fraction \frac{5962}{944} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{2981}{472}}$$

Rewrite the square root of the division \sqrt{\frac{2981}{472}} as the division of square roots \frac{\sqrt{2981}}{\sqrt{472}}.

$$\frac{\sqrt{2981}}{\sqrt{472}}$$

Factor 472=2^{2}\times 118. Rewrite the square root of the product \sqrt{2^{2}\times 118} as the product of square roots \sqrt{2^{2}}\sqrt{118}. Take the square root of 2^{2}.

$$\frac{\sqrt{2981}}{2\sqrt{118}}$$

Rationalize the denominator of \frac{\sqrt{2981}}{2\sqrt{118}} by multiplying numerator and denominator by \sqrt{118}.

$$\frac{\sqrt{2981}\sqrt{118}}{2\left(\sqrt{118}\right)^{2}}$$

The square of \sqrt{118} is 118.

$$\frac{\sqrt{2981}\sqrt{118}}{2\times 118}$$

To multiply \sqrt{2981} and \sqrt{118}, multiply the numbers under the square root.

$$\frac{\sqrt{351758}}{2\times 118}$$

Multiply 2 and 118 to get 236.

$$\frac{\sqrt{351758}}{236}$$