Solve 3frac{sqrt{2}}{3}frac{sqrt{10}}{2}

$$3 \frac{ \sqrt{ 2 } }{ 3 } \frac{ \sqrt{ 10 } }{ 2 }$$

Evaluate

$$\sqrt{5}\approx 2.236067977$$

Solution Steps

Cancel out 3 and 3.

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

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

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

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}.

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

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

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

Cancel out 2 and 2.

$$\sqrt{5}$$