Solve frac{16sqrt{56}}{2sqrt{2}}

$$\frac { 16 \sqrt { 56 } } { 2 \sqrt { 2 } }$$

Evaluate

$$16\sqrt{7}\approx 42.332020977$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{8\sqrt{56}}{\sqrt{2}}$$

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}.

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

Multiply 8 and 2 to get 16.

$$\frac{16\sqrt{14}}{\sqrt{2}}$$

Rationalize the denominator of \frac{16\sqrt{14}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$\frac{16\sqrt{14}\sqrt{2}}{2}$$

Factor 14=2\times 7. Rewrite the square root of the product \sqrt{2\times 7} as the product of square roots \sqrt{2}\sqrt{7}.

$$\frac{16\sqrt{2}\sqrt{7}\sqrt{2}}{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{16\times 2\sqrt{7}}{2}$$

Cancel out 2 and 2.

$$16\sqrt{7}$$