Solve frac{8sqrt{60}}{sqrt{28}}

$$\frac { 8 \sqrt { 60 } } { \sqrt { 28 } }$$

Evaluate

$$\frac{8\sqrt{105}}{7}\approx 11.710800875$$

Solution Steps

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$\frac{8\times 2\sqrt{15}}{\sqrt{28}}$$

Multiply 8 and 2 to get 16.

$$\frac{16\sqrt{15}}{\sqrt{28}}$$

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}.

$$\frac{16\sqrt{15}}{2\sqrt{7}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{8\sqrt{15}}{\sqrt{7}}$$

Rationalize the denominator of \frac{8\sqrt{15}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{8\sqrt{15}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{8\sqrt{15}\sqrt{7}}{7}$$

To multiply \sqrt{15} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{8\sqrt{105}}{7}$$