Solve sqrt{10}*sqrt{25/2}

$$\sqrt{ 10 } \times \sqrt{ \frac{ 25 }{ 2 } }$$

Evaluate

$$5\sqrt{5}\approx 11.180339887$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{25}{2}} as the division of square roots \frac{\sqrt{25}}{\sqrt{2}}.

$$\sqrt{10}\times \frac{\sqrt{25}}{\sqrt{2}}$$

Calculate the square root of 25 and get 5.

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

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

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

The square of \sqrt{2} is 2.

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

Express \sqrt{10}\times \frac{5\sqrt{2}}{2} as a single fraction.

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

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

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

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

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

Multiply 2 and 5 to get 10.

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

Divide 10\sqrt{5} by 2 to get 5\sqrt{5}.

$$5\sqrt{5}$$