Solve sqrt{24^2/24012*10^-7}

$$\sqrt { \frac { 24 ^ { 2 } } { 24012 \times 10 ^ { - 7 } } }$$

Evaluate

$$\frac{4000\sqrt{6670}}{667}\approx 489.775519978$$

Solution Steps

Calculate 24 to the power of 2 and get 576.

$$\sqrt{\frac{576}{24012\times 10^{-7}}}$$

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$\sqrt{\frac{576}{24012\times \frac{1}{10000000}}}$$

Multiply 24012 and \frac{1}{10000000} to get \frac{6003}{2500000}.

$$\sqrt{\frac{576}{\frac{6003}{2500000}}}$$

Divide 576 by \frac{6003}{2500000} by multiplying 576 by the reciprocal of \frac{6003}{2500000}.

$$\sqrt{576\times \frac{2500000}{6003}}$$

Multiply 576 and \frac{2500000}{6003} to get \frac{160000000}{667}.

$$\sqrt{\frac{160000000}{667}}$$

Rewrite the square root of the division \sqrt{\frac{160000000}{667}} as the division of square roots \frac{\sqrt{160000000}}{\sqrt{667}}.

$$\frac{\sqrt{160000000}}{\sqrt{667}}$$

Factor 160000000=4000^{2}\times 10. Rewrite the square root of the product \sqrt{4000^{2}\times 10} as the product of square roots \sqrt{4000^{2}}\sqrt{10}. Take the square root of 4000^{2}.

$$\frac{4000\sqrt{10}}{\sqrt{667}}$$

Rationalize the denominator of \frac{4000\sqrt{10}}{\sqrt{667}} by multiplying numerator and denominator by \sqrt{667}.

$$\frac{4000\sqrt{10}\sqrt{667}}{\left(\sqrt{667}\right)^{2}}$$

The square of \sqrt{667} is 667.

$$\frac{4000\sqrt{10}\sqrt{667}}{667}$$

To multiply \sqrt{10} and \sqrt{667}, multiply the numbers under the square root.

$$\frac{4000\sqrt{6670}}{667}$$