Solve frac{3sqrt{10}}{10}*frac{2sqrt{5}}{5}

$$\frac { 3 \sqrt { 10 } } { 10 } \times \frac { 2 \sqrt { 5 } } { 5 }$$

Evaluate

$$\frac{3\sqrt{2}}{5}\approx 0.848528137$$

Solution Steps

Multiply \frac{3\sqrt{10}}{10} times \frac{2\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\sqrt{10}\times 2\sqrt{5}}{10\times 5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\sqrt{5}\sqrt{10}}{5\times 5}$$

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}.

$$\frac{3\sqrt{5}\sqrt{5}\sqrt{2}}{5\times 5}$$

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

$$\frac{3\times 5\sqrt{2}}{5\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{15\sqrt{2}}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$\frac{15\sqrt{2}}{25}$$

Divide 15\sqrt{2} by 25 to get \frac{3}{5}\sqrt{2}.

$$\frac{3}{5}\sqrt{2}$$