Solve sqrt{256div6}

$$\sqrt{ 256 \div 6 }$$

Evaluate

$$\frac{8\sqrt{6}}{3}\approx 6.531972647$$

Solution Steps

Reduce the fraction \frac{256}{6} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{128}{3}}$$

Rewrite the square root of the division \sqrt{\frac{128}{3}} as the division of square roots \frac{\sqrt{128}}{\sqrt{3}}.

$$\frac{\sqrt{128}}{\sqrt{3}}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$\frac{8\sqrt{2}}{\sqrt{3}}$$

Rationalize the denominator of \frac{8\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{8\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{8\sqrt{2}\sqrt{3}}{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{8\sqrt{6}}{3}$$