Solve sqrt{400*10^-6*600*10^-12}

$$\sqrt{ 400 \times { 10 }^{ -6 } \times 600 \times { 10 }^{ -12 } }$$

Evaluate

$$\frac{\sqrt{6}}{5000000}\approx 0.00000049$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -6 and -12 to get -18.

$$\sqrt{400\times 10^{-18}\times 600}$$

Calculate 10 to the power of -18 and get \frac{1}{1000000000000000000}.

$$\sqrt{400\times \frac{1}{1000000000000000000}\times 600}$$

Multiply 400 and \frac{1}{1000000000000000000} to get \frac{1}{2500000000000000}.

$$\sqrt{\frac{1}{2500000000000000}\times 600}$$

Multiply \frac{1}{2500000000000000} and 600 to get \frac{3}{12500000000000}.

$$\sqrt{\frac{3}{12500000000000}}$$

Rewrite the square root of the division \sqrt{\frac{3}{12500000000000}} as the division of square roots \frac{\sqrt{3}}{\sqrt{12500000000000}}.

$$\frac{\sqrt{3}}{\sqrt{12500000000000}}$$

Factor 12500000000000=2500000^{2}\times 2. Rewrite the square root of the product \sqrt{2500000^{2}\times 2} as the product of square roots \sqrt{2500000^{2}}\sqrt{2}. Take the square root of 2500000^{2}.

$$\frac{\sqrt{3}}{2500000\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{3}}{2500000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{3}\sqrt{2}}{2500000\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{3}\sqrt{2}}{2500000\times 2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{2500000\times 2}$$

Multiply 2500000 and 2 to get 5000000.

$$\frac{\sqrt{6}}{5000000}$$