Solve (sqrt{80}+sqrt{80})divsqrt{5}

$$( \sqrt { 80 } + \sqrt { 80 } ) \div \sqrt { 5 }$$

Evaluate

$$8$$

Solution Steps

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$\frac{4\sqrt{5}+\sqrt{80}}{\sqrt{5}}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$\frac{4\sqrt{5}+4\sqrt{5}}{\sqrt{5}}$$

Combine 4\sqrt{5} and 4\sqrt{5} to get 8\sqrt{5}.

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

Rationalize the denominator of \frac{8\sqrt{5}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{8\sqrt{5}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

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

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

Multiply 8 and 5 to get 40.

$$\frac{40}{5}$$

Divide 40 by 5 to get 8.

$$8$$

Factor

$$2^{3}$$