Solve sqrt{8,7*10^-9/2}

$$\sqrt { \frac { 8,7 \times 10 ^ { - 9 } } { 2 } }$$

Evaluate

$$\frac{\sqrt{174}}{200000}\approx 0.000065955$$

Solution Steps

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$\sqrt{\frac{8,7\times \frac{1}{1000000000}}{2}}$$

Multiply 8,7 and \frac{1}{1000000000} to get \frac{87}{10000000000}.

$$\sqrt{\frac{\frac{87}{10000000000}}{2}}$$

Express \frac{\frac{87}{10000000000}}{2} as a single fraction.

$$\sqrt{\frac{87}{10000000000\times 2}}$$

Multiply 10000000000 and 2 to get 20000000000.

$$\sqrt{\frac{87}{20000000000}}$$

Rewrite the square root of the division \sqrt{\frac{87}{20000000000}} as the division of square roots \frac{\sqrt{87}}{\sqrt{20000000000}}.

$$\frac{\sqrt{87}}{\sqrt{20000000000}}$$

Factor 20000000000=100000^{2}\times 2. Rewrite the square root of the product \sqrt{100000^{2}\times 2} as the product of square roots \sqrt{100000^{2}}\sqrt{2}. Take the square root of 100000^{2}.

$$\frac{\sqrt{87}}{100000\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{87}}{100000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{87}\sqrt{2}}{100000\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{87}\sqrt{2}}{100000\times 2}$$

To multiply \sqrt{87} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{174}}{100000\times 2}$$

Multiply 100000 and 2 to get 200000.

$$\frac{\sqrt{174}}{200000}$$