Solve (sqrt{8}0+sqrt{40})divsqrt{5}

$$( \sqrt { 8 } 0 + \sqrt { 40 } ) \div \sqrt { 5 }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

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

$$\frac{0\times 2\sqrt{2}+\sqrt{40}}{\sqrt{5}}$$

Multiply 0 and 2 to get 0.

$$\frac{0\sqrt{2}+\sqrt{40}}{\sqrt{5}}$$

Anything times zero gives zero.

$$\frac{0+\sqrt{40}}{\sqrt{5}}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{0+2\sqrt{10}}{\sqrt{5}}$$

Anything plus zero gives itself.

$$\frac{2\sqrt{10}}{\sqrt{5}}$$

Rationalize the denominator of \frac{2\sqrt{10}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2\sqrt{10}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{10}\sqrt{5}}{5}$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

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

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

$$\frac{2\times 5\sqrt{2}}{5}$$

Cancel out 5 and 5.

$$2\sqrt{2}$$