Solve sqrt{(5*10^-3)(324)/9*10^9}

$$\sqrt{ \frac{ (5 \times { 10 }^{ -3 } )(324) }{ 9 \times { 10 }^{ 9 } } }$$

Evaluate

$$\frac{3\sqrt{5}}{500000}\approx 0.000013416$$

Solution Steps

Cancel out 9 in both numerator and denominator.

$$\sqrt{\frac{5\times 36\times 10^{-3}}{10^{9}}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\sqrt{\frac{5\times 36}{10^{12}}}$$

Multiply 5 and 36 to get 180.

$$\sqrt{\frac{180}{10^{12}}}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$\sqrt{\frac{180}{1000000000000}}$$

Reduce the fraction \frac{180}{1000000000000} to lowest terms by extracting and canceling out 20.

$$\sqrt{\frac{9}{50000000000}}$$

Rewrite the square root of the division \sqrt{\frac{9}{50000000000}} as the division of square roots \frac{\sqrt{9}}{\sqrt{50000000000}}.

$$\frac{\sqrt{9}}{\sqrt{50000000000}}$$

Calculate the square root of 9 and get 3.

$$\frac{3}{\sqrt{50000000000}}$$

Factor 50000000000=100000^{2}\times 5. Rewrite the square root of the product \sqrt{100000^{2}\times 5} as the product of square roots \sqrt{100000^{2}}\sqrt{5}. Take the square root of 100000^{2}.

$$\frac{3}{100000\sqrt{5}}$$

Rationalize the denominator of \frac{3}{100000\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{3\sqrt{5}}{100000\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{3\sqrt{5}}{100000\times 5}$$

Multiply 100000 and 5 to get 500000.

$$\frac{3\sqrt{5}}{500000}$$