Solve sqrt{(0.8)(0.1)^2/9*10^9}

$$\sqrt { \frac { ( 0.8 ) ( 0.1 ) ^ { 2 } } { 9 \times 10 ^ { 9 } } }$$

Evaluate

$$\frac{\sqrt{2}}{1500000}\approx 0.000000943$$

Solution Steps

Calculate 0.1 to the power of 2 and get 0.01.

$$\sqrt{\frac{0.8\times 0.01}{9\times 10^{9}}}$$

Multiply 0.8 and 0.01 to get 0.008.

$$\sqrt{\frac{0.008}{9\times 10^{9}}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\sqrt{\frac{0.008}{9\times 1000000000}}$$

Multiply 9 and 1000000000 to get 9000000000.

$$\sqrt{\frac{0.008}{9000000000}}$$

Expand \frac{0.008}{9000000000} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{8}{9000000000000}}$$

Reduce the fraction \frac{8}{9000000000000} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{1}{1125000000000}}$$

Rewrite the square root of the division \sqrt{\frac{1}{1125000000000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{1125000000000}}.

$$\frac{\sqrt{1}}{\sqrt{1125000000000}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{1125000000000}}$$

Factor 1125000000000=750000^{2}\times 2. Rewrite the square root of the product \sqrt{750000^{2}\times 2} as the product of square roots \sqrt{750000^{2}}\sqrt{2}. Take the square root of 750000^{2}.

$$\frac{1}{750000\sqrt{2}}$$

Rationalize the denominator of \frac{1}{750000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}}{750000\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{750000\times 2}$$

Multiply 750000 and 2 to get 1500000.

$$\frac{\sqrt{2}}{1500000}$$