Solve sqrt{256div5*7}

$$\sqrt{ 256 \div 5 \times 7 }$$

Evaluate

$$\frac{16\sqrt{35}}{5}\approx 18.931455306$$

Solution Steps

Express \frac{256}{5}\times 7 as a single fraction.

$$\sqrt{\frac{256\times 7}{5}}$$

Multiply 256 and 7 to get 1792.

$$\sqrt{\frac{1792}{5}}$$

Rewrite the square root of the division \sqrt{\frac{1792}{5}} as the division of square roots \frac{\sqrt{1792}}{\sqrt{5}}.

$$\frac{\sqrt{1792}}{\sqrt{5}}$$

Factor 1792=16^{2}\times 7. Rewrite the square root of the product \sqrt{16^{2}\times 7} as the product of square roots \sqrt{16^{2}}\sqrt{7}. Take the square root of 16^{2}.

$$\frac{16\sqrt{7}}{\sqrt{5}}$$

Rationalize the denominator of \frac{16\sqrt{7}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{16\sqrt{7}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{16\sqrt{7}\sqrt{5}}{5}$$

To multiply \sqrt{7} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{16\sqrt{35}}{5}$$