Solve sqrt{(60div7)}

$$\sqrt{ (60 \div 7) }$$

Evaluate

$$\frac{2\sqrt{105}}{7}\approx 2.927700219$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{60}{7}} as the division of square roots \frac{\sqrt{60}}{\sqrt{7}}.

$$\frac{\sqrt{60}}{\sqrt{7}}$$

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}.

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

Rationalize the denominator of \frac{2\sqrt{15}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

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

The square of \sqrt{7} is 7.

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

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

$$\frac{2\sqrt{105}}{7}$$