Solve frac{sqrt{28}*sqrt{147}}{sqrt{187}}

$$\frac { \sqrt { 28 } \times \sqrt { 147 } } { \sqrt { 187 } }$$

Evaluate

$$\frac{14\sqrt{3927}}{187}\approx 4.691555732$$

Solution Steps

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$\frac{2\sqrt{7}\sqrt{147}}{\sqrt{187}}$$

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$\frac{2\sqrt{7}\times 7\sqrt{3}}{\sqrt{187}}$$

Multiply 2 and 7 to get 14.

$$\frac{14\sqrt{7}\sqrt{3}}{\sqrt{187}}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{14\sqrt{21}}{\sqrt{187}}$$

Rationalize the denominator of \frac{14\sqrt{21}}{\sqrt{187}} by multiplying numerator and denominator by \sqrt{187}.

$$\frac{14\sqrt{21}\sqrt{187}}{\left(\sqrt{187}\right)^{2}}$$

The square of \sqrt{187} is 187.

$$\frac{14\sqrt{21}\sqrt{187}}{187}$$

To multiply \sqrt{21} and \sqrt{187}, multiply the numbers under the square root.

$$\frac{14\sqrt{3927}}{187}$$