Solve sqrt{5}*sqrt{10}divsqrt{2}

$$\sqrt { 5 } \times \sqrt { 10 } \div \sqrt { 2 }$$

Evaluate

$$5$$

Solution Steps

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}.

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

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

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Multiply 5 and 2 to get 10.

$$\frac{10}{2}$$

Divide 10 by 2 to get 5.

$$5$$

Factor

$$5$$