Solve 3sqrt{0.6/1296*0.94}

$$3 \sqrt{ \frac{ 0.6 }{ 1296 } \times 0.94 }$$

Evaluate

$$\frac{\sqrt{1410}}{600}\approx 0.062583278$$

Solution Steps

Expand \frac{0.6}{1296} by multiplying both numerator and the denominator by 10.

$$3\sqrt{\frac{6}{12960}\times 0.94}$$

Reduce the fraction \frac{6}{12960} to lowest terms by extracting and canceling out 6.

$$3\sqrt{\frac{1}{2160}\times 0.94}$$

Convert decimal number 0.94 to fraction \frac{94}{100}. Reduce the fraction \frac{94}{100} to lowest terms by extracting and canceling out 2.

$$3\sqrt{\frac{1}{2160}\times \frac{47}{50}}$$

Multiply \frac{1}{2160} times \frac{47}{50} by multiplying numerator times numerator and denominator times denominator.

$$3\sqrt{\frac{1\times 47}{2160\times 50}}$$

Do the multiplications in the fraction \frac{1\times 47}{2160\times 50}.

$$3\sqrt{\frac{47}{108000}}$$

Rewrite the square root of the division \sqrt{\frac{47}{108000}} as the division of square roots \frac{\sqrt{47}}{\sqrt{108000}}.

$$3\times \frac{\sqrt{47}}{\sqrt{108000}}$$

Factor 108000=60^{2}\times 30. Rewrite the square root of the product \sqrt{60^{2}\times 30} as the product of square roots \sqrt{60^{2}}\sqrt{30}. Take the square root of 60^{2}.

$$3\times \frac{\sqrt{47}}{60\sqrt{30}}$$

Rationalize the denominator of \frac{\sqrt{47}}{60\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$3\times \frac{\sqrt{47}\sqrt{30}}{60\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$3\times \frac{\sqrt{47}\sqrt{30}}{60\times 30}$$

To multiply \sqrt{47} and \sqrt{30}, multiply the numbers under the square root.

$$3\times \frac{\sqrt{1410}}{60\times 30}$$

Multiply 60 and 30 to get 1800.

$$3\times \frac{\sqrt{1410}}{1800}$$

Cancel out 1800, the greatest common factor in 3 and 1800.

$$\frac{\sqrt{1410}}{600}$$