Solve sqrt{4.0*10^-24/1.8*10^-5}

$$\sqrt{ \frac{ 4.0 \times { 10 }^{ -24 } }{ 1.8 \times { 10 }^{ -5 } } }$$

Evaluate

$$\frac{\sqrt{2}}{3000000000}\approx 4.714045208 \cdot 10^{-10}$$

Solution Steps

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

$$\sqrt{\frac{4}{1.8\times 10^{19}}}$$

Calculate 10 to the power of 19 and get 10000000000000000000.

$$\sqrt{\frac{4}{1.8\times 10000000000000000000}}$$

Multiply 1.8 and 10000000000000000000 to get 18000000000000000000.

$$\sqrt{\frac{4}{18000000000000000000}}$$

Reduce the fraction \frac{4}{18000000000000000000} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{1}{4500000000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{1}{4500000000000000000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{4500000000000000000}}.

$$\frac{\sqrt{1}}{\sqrt{4500000000000000000}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{4500000000000000000}}$$

Factor 4500000000000000000=1500000000^{2}\times 2. Rewrite the square root of the product \sqrt{1500000000^{2}\times 2} as the product of square roots \sqrt{1500000000^{2}}\sqrt{2}. Take the square root of 1500000000^{2}.

$$\frac{1}{1500000000\sqrt{2}}$$

Rationalize the denominator of \frac{1}{1500000000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}}{1500000000\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{1500000000\times 2}$$

Multiply 1500000000 and 2 to get 3000000000.

$$\frac{\sqrt{2}}{3000000000}$$