Solve 4/3sqrt{20}

$$\frac { 4 } { 3 \sqrt { 20 } }$$

Evaluate

$$\frac{2\sqrt{5}}{15}\approx 0.298142397$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{4}{3\times 2\sqrt{5}}$$

Multiply 3 and 2 to get 6.

$$\frac{4}{6\sqrt{5}}$$

Rationalize the denominator of \frac{4}{6\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{4\sqrt{5}}{6\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{4\sqrt{5}}{6\times 5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\sqrt{5}}{3\times 5}$$

Multiply 3 and 5 to get 15.

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