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

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

Evaluate

$$\frac{2\sqrt{5}}{5}\approx 0.894427191$$

Solution Steps

Combine 3\sqrt{10} and \sqrt{10} to get 4\sqrt{10}.

$$\frac{4\sqrt{10}}{10\sqrt{2}}$$

Cancel out 2 in both numerator and denominator.

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

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

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

The square of \sqrt{2} is 2.

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

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}.

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

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

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

Multiply 5 and 2 to get 10.

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

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{5}}{10}$$

Divide 4\sqrt{5} by 10 to get \frac{2}{5}\sqrt{5}.

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