Solve 3*sqrt{0.6/1296*0.96}

$$3 \times \sqrt{ \frac{ 0.6 }{ 1296 } \times 0.96 }$$

Evaluate

$$\frac{\sqrt{10}}{50}\approx 0.063245553$$

Solution Steps

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

$$3\sqrt{\frac{6}{12960}\times 0.96}$$

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

$$3\sqrt{\frac{1}{2160}\times 0.96}$$

Convert decimal number 0.96 to fraction \frac{96}{100}. Reduce the fraction \frac{96}{100} to lowest terms by extracting and canceling out 4.

$$3\sqrt{\frac{1}{2160}\times \frac{24}{25}}$$

Multiply \frac{1}{2160} times \frac{24}{25} by multiplying numerator times numerator and denominator times denominator.

$$3\sqrt{\frac{1\times 24}{2160\times 25}}$$

Do the multiplications in the fraction \frac{1\times 24}{2160\times 25}.

$$3\sqrt{\frac{24}{54000}}$$

Reduce the fraction \frac{24}{54000} to lowest terms by extracting and canceling out 24.

$$3\sqrt{\frac{1}{2250}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2250}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2250}}.

$$3\times \frac{\sqrt{1}}{\sqrt{2250}}$$

Calculate the square root of 1 and get 1.

$$3\times \frac{1}{\sqrt{2250}}$$

Factor 2250=15^{2}\times 10. Rewrite the square root of the product \sqrt{15^{2}\times 10} as the product of square roots \sqrt{15^{2}}\sqrt{10}. Take the square root of 15^{2}.

$$3\times \frac{1}{15\sqrt{10}}$$

Rationalize the denominator of \frac{1}{15\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$3\times \frac{\sqrt{10}}{15\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$3\times \frac{\sqrt{10}}{15\times 10}$$

Multiply 15 and 10 to get 150.

$$3\times \frac{\sqrt{10}}{150}$$

Cancel out 150, the greatest common factor in 3 and 150.

$$\frac{\sqrt{10}}{50}$$