Solve sqrt{1/72*10^-7*10^17*1000}

$$\sqrt { \frac { 1 } { 72 \times 10 ^ { - 7 } \times 10 ^ { 17 } \times 1000 } }$$

Evaluate

$$\frac{\sqrt{5}}{60000000}\approx 0.000000037$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -7 and 17 to get 10.

$$\sqrt{\frac{1}{72\times 10^{10}\times 1000}}$$

Calculate 10 to the power of 10 and get 10000000000.

$$\sqrt{\frac{1}{72\times 10000000000\times 1000}}$$

Multiply 72 and 10000000000 to get 720000000000.

$$\sqrt{\frac{1}{720000000000\times 1000}}$$

Multiply 720000000000 and 1000 to get 720000000000000.

$$\sqrt{\frac{1}{720000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{1}{720000000000000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{720000000000000}}.

$$\frac{\sqrt{1}}{\sqrt{720000000000000}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{720000000000000}}$$

Factor 720000000000000=12000000^{2}\times 5. Rewrite the square root of the product \sqrt{12000000^{2}\times 5} as the product of square roots \sqrt{12000000^{2}}\sqrt{5}. Take the square root of 12000000^{2}.

$$\frac{1}{12000000\sqrt{5}}$$

Rationalize the denominator of \frac{1}{12000000\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{12000000\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}}{12000000\times 5}$$

Multiply 12000000 and 5 to get 60000000.

$$\frac{\sqrt{5}}{60000000}$$