Solve frac{14sqrt{320}}{2sqrt{5}}

$$\frac{ 14 \sqrt{ 320 } }{ 2 \sqrt{ 5 } }$$

Evaluate

$$56$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{7\sqrt{320}}{\sqrt{5}}$$

Factor 320=8^{2}\times 5. Rewrite the square root of the product \sqrt{8^{2}\times 5} as the product of square roots \sqrt{8^{2}}\sqrt{5}. Take the square root of 8^{2}.

$$\frac{7\times 8\sqrt{5}}{\sqrt{5}}$$

Multiply 7 and 8 to get 56.

$$\frac{56\sqrt{5}}{\sqrt{5}}$$

Rationalize the denominator of \frac{56\sqrt{5}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{56\sqrt{5}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{56\sqrt{5}\sqrt{5}}{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{56\times 5}{5}$$

Multiply 56 and 5 to get 280.

$$\frac{280}{5}$$

Divide 280 by 5 to get 56.

$$56$$

Factor

$$2^{3}\times 7$$