Solve frac{5sqrt{2}}{15sqrt{40}}

$$\frac { 5 \sqrt { 2 } } { 15 \sqrt { 40 } }$$

Evaluate

$$\frac{\sqrt{5}}{30}\approx 0.074535599$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$\frac{\sqrt{2}}{3\sqrt{40}}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

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

Multiply 3 and 2 to get 6.

$$\frac{\sqrt{2}}{6\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{2}}{6\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{2}\sqrt{10}}{6\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{2}\sqrt{10}}{6\times 10}$$

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}.

$$\frac{\sqrt{2}\sqrt{2}\sqrt{5}}{6\times 10}$$

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

$$\frac{2\sqrt{5}}{6\times 10}$$

Multiply 6 and 10 to get 60.

$$\frac{2\sqrt{5}}{60}$$

Divide 2\sqrt{5} by 60 to get \frac{1}{30}\sqrt{5}.

$$\frac{1}{30}\sqrt{5}$$