Solve frac{sqrt{8}}{3sqrt{40}}sqrt{5}

$$\frac{ \sqrt{ 8 } }{ 3 \sqrt{ 40 } } \sqrt{ 5 }$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{2\sqrt{2}}{3\sqrt{40}}\sqrt{5}$$

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}.

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

Multiply 3 and 2 to get 6.

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

Cancel out 2 in both numerator and denominator.

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

Rationalize the denominator of \frac{\sqrt{2}}{3\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{2}\sqrt{10}}{3\left(\sqrt{10}\right)^{2}}\sqrt{5}$$

The square of \sqrt{10} is 10.

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

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}.

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

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

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

Multiply 3 and 10 to get 30.

$$\frac{2\sqrt{5}}{30}\sqrt{5}$$

Divide 2\sqrt{5} by 30 to get \frac{1}{15}\sqrt{5}.

$$\frac{1}{15}\sqrt{5}\sqrt{5}$$

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

$$\frac{1}{15}\times 5$$

Multiply \frac{1}{15} and 5 to get \frac{5}{15}.

$$\frac{5}{15}$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$