Solve sqrt{(3.7*10^-9)(5*10^-10)/(8.99*10^9)}

$$\sqrt{ \frac{ (3.7 \times { 10 }^{ -9 } )(5 \times { 10 }^{ -10 } ) }{ (8.99 \times { 10 }^{ 9 } ) } }$$

Evaluate

$$\frac{\sqrt{66526}}{17980000000000000}\approx 1.434518054 \cdot 10^{-14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -9 and -10 to get -19.

$$\sqrt{\frac{3.7\times 10^{-19}\times 5}{8.99\times 10^{9}}}$$

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

$$\sqrt{\frac{3.7\times 5}{8.99\times 10^{28}}}$$

Multiply 3.7 and 5 to get 18.5.

$$\sqrt{\frac{18.5}{8.99\times 10^{28}}}$$

Calculate 10 to the power of 28 and get 10000000000000000000000000000.

$$\sqrt{\frac{18.5}{8.99\times 10000000000000000000000000000}}$$

Multiply 8.99 and 10000000000000000000000000000 to get 89900000000000000000000000000.

$$\sqrt{\frac{18.5}{89900000000000000000000000000}}$$

Expand \frac{18.5}{89900000000000000000000000000} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{185}{899000000000000000000000000000}}$$

Reduce the fraction \frac{185}{899000000000000000000000000000} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{37}{179800000000000000000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{37}{179800000000000000000000000000}} as the division of square roots \frac{\sqrt{37}}{\sqrt{179800000000000000000000000000}}.

$$\frac{\sqrt{37}}{\sqrt{179800000000000000000000000000}}$$

Factor 179800000000000000000000000000=10000000000000^{2}\times 1798. Rewrite the square root of the product \sqrt{10000000000000^{2}\times 1798} as the product of square roots \sqrt{10000000000000^{2}}\sqrt{1798}. Take the square root of 10000000000000^{2}.

$$\frac{\sqrt{37}}{10000000000000\sqrt{1798}}$$

Rationalize the denominator of \frac{\sqrt{37}}{10000000000000\sqrt{1798}} by multiplying numerator and denominator by \sqrt{1798}.

$$\frac{\sqrt{37}\sqrt{1798}}{10000000000000\left(\sqrt{1798}\right)^{2}}$$

The square of \sqrt{1798} is 1798.

$$\frac{\sqrt{37}\sqrt{1798}}{10000000000000\times 1798}$$

To multiply \sqrt{37} and \sqrt{1798}, multiply the numbers under the square root.

$$\frac{\sqrt{66526}}{10000000000000\times 1798}$$

Multiply 10000000000000 and 1798 to get 17980000000000000.

$$\frac{\sqrt{66526}}{17980000000000000}$$