Solve sqrt{2*3.835*10^-5*20*0.5*10^-3}=

$$\sqrt { 2 \times 3.835 \times 10 ^ { - 5 } \times 20 \times 0.5 \times 10 ^ { - 3 } } =$$

Evaluate

$$\frac{\sqrt{7670}}{100000}\approx 0.000875785$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -5 and -3 to get -8.

$$\sqrt{2\times 3.835\times 10^{-8}\times 20\times 0.5}$$

Multiply 2 and 3.835 to get 7.67.

$$\sqrt{7.67\times 10^{-8}\times 20\times 0.5}$$

Calculate 10 to the power of -8 and get \frac{1}{100000000}.

$$\sqrt{7.67\times \frac{1}{100000000}\times 20\times 0.5}$$

Multiply 7.67 and \frac{1}{100000000} to get \frac{767}{10000000000}.

$$\sqrt{\frac{767}{10000000000}\times 20\times 0.5}$$

Multiply \frac{767}{10000000000} and 20 to get \frac{767}{500000000}.

$$\sqrt{\frac{767}{500000000}\times 0.5}$$

Multiply \frac{767}{500000000} and 0.5 to get \frac{767}{1000000000}.

$$\sqrt{\frac{767}{1000000000}}$$

Rewrite the square root of the division \sqrt{\frac{767}{1000000000}} as the division of square roots \frac{\sqrt{767}}{\sqrt{1000000000}}.

$$\frac{\sqrt{767}}{\sqrt{1000000000}}$$

Factor 1000000000=10000^{2}\times 10. Rewrite the square root of the product \sqrt{10000^{2}\times 10} as the product of square roots \sqrt{10000^{2}}\sqrt{10}. Take the square root of 10000^{2}.

$$\frac{\sqrt{767}}{10000\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{767}}{10000\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{767}\sqrt{10}}{10000\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{767}\sqrt{10}}{10000\times 10}$$

To multiply \sqrt{767} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{7670}}{10000\times 10}$$

Multiply 10000 and 10 to get 100000.

$$\frac{\sqrt{7670}}{100000}$$