Solve sqrt{8/45}

$$\sqrt { \frac { 8 } { 45 } }$$

Evaluate

$$\frac{2\sqrt{10}}{15}\approx 0.421637021$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{8}{45}} as the division of square roots \frac{\sqrt{8}}{\sqrt{45}}.

$$\frac{\sqrt{8}}{\sqrt{45}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{2\sqrt{2}}{\sqrt{45}}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

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

Rationalize the denominator of \frac{2\sqrt{2}}{3\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2\sqrt{2}\sqrt{5}}{3\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{2\sqrt{10}}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{2\sqrt{10}}{15}$$