Solve sqrt{32/213}

$$\sqrt{ \frac{ 32 }{ 213 } }$$

Evaluate

$$\frac{4\sqrt{426}}{213}\approx 0.387601266$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{32}{213}} as the division of square roots \frac{\sqrt{32}}{\sqrt{213}}.

$$\frac{\sqrt{32}}{\sqrt{213}}$$

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}.

$$\frac{4\sqrt{2}}{\sqrt{213}}$$

Rationalize the denominator of \frac{4\sqrt{2}}{\sqrt{213}} by multiplying numerator and denominator by \sqrt{213}.

$$\frac{4\sqrt{2}\sqrt{213}}{\left(\sqrt{213}\right)^{2}}$$

The square of \sqrt{213} is 213.

$$\frac{4\sqrt{2}\sqrt{213}}{213}$$

To multiply \sqrt{2} and \sqrt{213}, multiply the numbers under the square root.

$$\frac{4\sqrt{426}}{213}$$