Solve 1/67.2sqrt{985*1000/0.00057}

$$\frac { 1 } { 67.2 } \sqrt { \frac { 985 \times 1000 } { 0.00057 } }$$

Evaluate

$$\frac{3125\sqrt{56145}}{1197}\approx 618.602134709$$

Solution Steps

Expand \frac{1}{67.2} by multiplying both numerator and the denominator by 10.

$$\frac{10}{672}\sqrt{\frac{985\times 1000}{0.00057}}$$

Reduce the fraction \frac{10}{672} to lowest terms by extracting and canceling out 2.

$$\frac{5}{336}\sqrt{\frac{985\times 1000}{0.00057}}$$

Multiply 985 and 1000 to get 985000.

$$\frac{5}{336}\sqrt{\frac{985000}{0.00057}}$$

Expand \frac{985000}{0.00057} by multiplying both numerator and the denominator by 100000.

$$\frac{5}{336}\sqrt{\frac{98500000000}{57}}$$

Rewrite the square root of the division \sqrt{\frac{98500000000}{57}} as the division of square roots \frac{\sqrt{98500000000}}{\sqrt{57}}.

$$\frac{5}{336}\times \frac{\sqrt{98500000000}}{\sqrt{57}}$$

Factor 98500000000=10000^{2}\times 985. Rewrite the square root of the product \sqrt{10000^{2}\times 985} as the product of square roots \sqrt{10000^{2}}\sqrt{985}. Take the square root of 10000^{2}.

$$\frac{5}{336}\times \frac{10000\sqrt{985}}{\sqrt{57}}$$

Rationalize the denominator of \frac{10000\sqrt{985}}{\sqrt{57}} by multiplying numerator and denominator by \sqrt{57}.

$$\frac{5}{336}\times \frac{10000\sqrt{985}\sqrt{57}}{\left(\sqrt{57}\right)^{2}}$$

The square of \sqrt{57} is 57.

$$\frac{5}{336}\times \frac{10000\sqrt{985}\sqrt{57}}{57}$$

To multiply \sqrt{985} and \sqrt{57}, multiply the numbers under the square root.

$$\frac{5}{336}\times \frac{10000\sqrt{56145}}{57}$$

Multiply \frac{5}{336} times \frac{10000\sqrt{56145}}{57} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 10000\sqrt{56145}}{336\times 57}$$

Cancel out 16 in both numerator and denominator.

$$\frac{5\times 625\sqrt{56145}}{21\times 57}$$

Multiply 5 and 625 to get 3125.

$$\frac{3125\sqrt{56145}}{21\times 57}$$

Multiply 21 and 57 to get 1197.

$$\frac{3125\sqrt{56145}}{1197}$$