Solve sqrt{27*11/49*18}

$$\sqrt { \frac { 27 \times 11 } { 49 \times 18 } }$$

Evaluate

$$\frac{\sqrt{66}}{14}\approx 0.580288457$$

Solution Steps

Cancel out 9 in both numerator and denominator.

$$\sqrt{\frac{3\times 11}{2\times 49}}$$

Multiply 3 and 11 to get 33.

$$\sqrt{\frac{33}{2\times 49}}$$

Multiply 2 and 49 to get 98.

$$\sqrt{\frac{33}{98}}$$

Rewrite the square root of the division \sqrt{\frac{33}{98}} as the division of square roots \frac{\sqrt{33}}{\sqrt{98}}.

$$\frac{\sqrt{33}}{\sqrt{98}}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$\frac{\sqrt{33}}{7\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{33}}{7\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{33}\sqrt{2}}{7\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{33}\sqrt{2}}{7\times 2}$$

To multiply \sqrt{33} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{66}}{7\times 2}$$

Multiply 7 and 2 to get 14.

$$\frac{\sqrt{66}}{14}$$