Solve frac{sqrt{28*139}}{sqrt{27*6}}

$$\frac { \sqrt { 28 \cdot 139 } } { \sqrt { 27 \cdot 6 } }$$

Evaluate

$$\frac{\sqrt{1946}}{9}\approx 4.901498889$$

Solution Steps

Multiply 28 and 139 to get 3892.

$$\frac{\sqrt{3892}}{\sqrt{27\times 6}}$$

Factor 3892=2^{2}\times 973. Rewrite the square root of the product \sqrt{2^{2}\times 973} as the product of square roots \sqrt{2^{2}}\sqrt{973}. Take the square root of 2^{2}.

$$\frac{2\sqrt{973}}{\sqrt{27\times 6}}$$

Multiply 27 and 6 to get 162.

$$\frac{2\sqrt{973}}{\sqrt{162}}$$

Factor 162=9^{2}\times 2. Rewrite the square root of the product \sqrt{9^{2}\times 2} as the product of square roots \sqrt{9^{2}}\sqrt{2}. Take the square root of 9^{2}.

$$\frac{2\sqrt{973}}{9\sqrt{2}}$$

Rationalize the denominator of \frac{2\sqrt{973}}{9\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{2\sqrt{973}\sqrt{2}}{9\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{2\sqrt{973}\sqrt{2}}{9\times 2}$$

To multiply \sqrt{973} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{2\sqrt{1946}}{9\times 2}$$

Multiply 9 and 2 to get 18.

$$\frac{2\sqrt{1946}}{18}$$

Divide 2\sqrt{1946} by 18 to get \frac{1}{9}\sqrt{1946}.

$$\frac{1}{9}\sqrt{1946}$$