Solve frac{4sqrt{60}}{2sqrt{5}}

$$\frac{ 4 \sqrt{ 60 } }{ 2 \sqrt{ 5 } }$$

Evaluate

$$4\sqrt{3}\approx 6.92820323$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{2\sqrt{60}}{\sqrt{5}}$$

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}.

$$\frac{2\times 2\sqrt{15}}{\sqrt{5}}$$

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{15}}{\sqrt{5}}$$

Rationalize the denominator of \frac{4\sqrt{15}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{4\sqrt{15}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{4\sqrt{15}\sqrt{5}}{5}$$

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

$$\frac{4\sqrt{5}\sqrt{3}\sqrt{5}}{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{4\times 5\sqrt{3}}{5}$$

Cancel out 5 and 5.

$$4\sqrt{3}$$