Solve 4sqrt{8/10^4}

$$4 \sqrt{ \frac{ 8 }{ { 10 }^{ 4 } } }$$

Evaluate

$$\frac{2\sqrt{2}}{25}\approx 0.113137085$$

Solution Steps

Calculate 10 to the power of 4 and get 10000.

$$4\sqrt{\frac{8}{10000}}$$

Reduce the fraction \frac{8}{10000} to lowest terms by extracting and canceling out 8.

$$4\sqrt{\frac{1}{1250}}$$

Rewrite the square root of the division \sqrt{\frac{1}{1250}} as the division of square roots \frac{\sqrt{1}}{\sqrt{1250}}.

$$4\times \frac{\sqrt{1}}{\sqrt{1250}}$$

Calculate the square root of 1 and get 1.

$$4\times \frac{1}{\sqrt{1250}}$$

Factor 1250=25^{2}\times 2. Rewrite the square root of the product \sqrt{25^{2}\times 2} as the product of square roots \sqrt{25^{2}}\sqrt{2}. Take the square root of 25^{2}.

$$4\times \frac{1}{25\sqrt{2}}$$

Rationalize the denominator of \frac{1}{25\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$4\times \frac{\sqrt{2}}{25\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$4\times \frac{\sqrt{2}}{25\times 2}$$

Multiply 25 and 2 to get 50.

$$4\times \frac{\sqrt{2}}{50}$$

Express 4\times \frac{\sqrt{2}}{50} as a single fraction.

$$\frac{4\sqrt{2}}{50}$$

Divide 4\sqrt{2} by 50 to get \frac{2}{25}\sqrt{2}.

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