Solve 8sqrt{56}*1/sqrt{14}

$$8 \sqrt { 56 } \times \frac { 1 } { \sqrt { 14 } }$$

Evaluate

$$16$$

Solution Steps

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$8\times 2\sqrt{14}\times \frac{1}{\sqrt{14}}$$

Multiply 8 and 2 to get 16.

$$16\sqrt{14}\times \frac{1}{\sqrt{14}}$$

Rationalize the denominator of \frac{1}{\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$16\sqrt{14}\times \frac{\sqrt{14}}{\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$16\sqrt{14}\times \frac{\sqrt{14}}{14}$$

Express 16\times \frac{\sqrt{14}}{14} as a single fraction.

$$\frac{16\sqrt{14}}{14}\sqrt{14}$$

Divide 16\sqrt{14} by 14 to get \frac{8}{7}\sqrt{14}.

$$\frac{8}{7}\sqrt{14}\sqrt{14}$$

Multiply \sqrt{14} and \sqrt{14} to get 14.

$$\frac{8}{7}\times 14$$

Express \frac{8}{7}\times 14 as a single fraction.

$$\frac{8\times 14}{7}$$

Multiply 8 and 14 to get 112.

$$\frac{112}{7}$$

Divide 112 by 7 to get 16.

$$16$$

Factor

$$2^{4}$$