Solve sqrt{274/612}

$$\sqrt { \frac { 274 } { 612 } }$$

Evaluate

$$\frac{\sqrt{4658}}{102}\approx 0.669113158$$

Solution Steps

Reduce the fraction \frac{274}{612} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{137}{306}}$$

Rewrite the square root of the division \sqrt{\frac{137}{306}} as the division of square roots \frac{\sqrt{137}}{\sqrt{306}}.

$$\frac{\sqrt{137}}{\sqrt{306}}$$

Factor 306=3^{2}\times 34. Rewrite the square root of the product \sqrt{3^{2}\times 34} as the product of square roots \sqrt{3^{2}}\sqrt{34}. Take the square root of 3^{2}.

$$\frac{\sqrt{137}}{3\sqrt{34}}$$

Rationalize the denominator of \frac{\sqrt{137}}{3\sqrt{34}} by multiplying numerator and denominator by \sqrt{34}.

$$\frac{\sqrt{137}\sqrt{34}}{3\left(\sqrt{34}\right)^{2}}$$

The square of \sqrt{34} is 34.

$$\frac{\sqrt{137}\sqrt{34}}{3\times 34}$$

To multiply \sqrt{137} and \sqrt{34}, multiply the numbers under the square root.

$$\frac{\sqrt{4658}}{3\times 34}$$

Multiply 3 and 34 to get 102.

$$\frac{\sqrt{4658}}{102}$$