Solve sqrt{32/125}=

$$\sqrt{ \frac{ 32 }{ 125 } } =$$

Evaluate

$$\frac{4\sqrt{10}}{25}\approx 0.505964426$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{32}{125}} as the division of square roots \frac{\sqrt{32}}{\sqrt{125}}.

$$\frac{\sqrt{32}}{\sqrt{125}}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{4\sqrt{2}}{\sqrt{125}}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

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

Rationalize the denominator of \frac{4\sqrt{2}}{5\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

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

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

$$\frac{4\sqrt{10}}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$\frac{4\sqrt{10}}{25}$$