Solve =sqrt{3985*10^8/42370}

$$= \sqrt { \frac { 3985 \times 10 ^ { 8 } } { 42370 } }$$

Evaluate

$$\frac{5000\sqrt{6753778}}{4237}\approx 3066.796301728$$

Solution Steps

Calculate 10 to the power of 8 and get 100000000.

$$\sqrt{\frac{3985\times 100000000}{42370}}$$

Multiply 3985 and 100000000 to get 398500000000.

$$\sqrt{\frac{398500000000}{42370}}$$

Reduce the fraction \frac{398500000000}{42370} to lowest terms by extracting and canceling out 10.

$$\sqrt{\frac{39850000000}{4237}}$$

Rewrite the square root of the division \sqrt{\frac{39850000000}{4237}} as the division of square roots \frac{\sqrt{39850000000}}{\sqrt{4237}}.

$$\frac{\sqrt{39850000000}}{\sqrt{4237}}$$

Factor 39850000000=5000^{2}\times 1594. Rewrite the square root of the product \sqrt{5000^{2}\times 1594} as the product of square roots \sqrt{5000^{2}}\sqrt{1594}. Take the square root of 5000^{2}.

$$\frac{5000\sqrt{1594}}{\sqrt{4237}}$$

Rationalize the denominator of \frac{5000\sqrt{1594}}{\sqrt{4237}} by multiplying numerator and denominator by \sqrt{4237}.

$$\frac{5000\sqrt{1594}\sqrt{4237}}{\left(\sqrt{4237}\right)^{2}}$$

The square of \sqrt{4237} is 4237.

$$\frac{5000\sqrt{1594}\sqrt{4237}}{4237}$$

To multiply \sqrt{1594} and \sqrt{4237}, multiply the numbers under the square root.

$$\frac{5000\sqrt{6753778}}{4237}$$