Solve sqrt{3*4.8^2/28.8^2}

$$\sqrt { \frac { 3 \times 4.8 ^ { 2 } } { 28.8 ^ { 2 } } }$$

Evaluate

$$\frac{\sqrt{3}}{6}\approx 0.288675135$$

Solution Steps

Calculate 4.8 to the power of 2 and get 23.04.

$$\sqrt{\frac{3\times 23.04}{28.8^{2}}}$$

Multiply 3 and 23.04 to get 69.12.

$$\sqrt{\frac{69.12}{28.8^{2}}}$$

Calculate 28.8 to the power of 2 and get 829.44.

$$\sqrt{\frac{69.12}{829.44}}$$

Expand \frac{69.12}{829.44} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{6912}{82944}}$$

Reduce the fraction \frac{6912}{82944} to lowest terms by extracting and canceling out 6912.

$$\sqrt{\frac{1}{12}}$$

Rewrite the square root of the division \sqrt{\frac{1}{12}} as the division of square roots \frac{\sqrt{1}}{\sqrt{12}}.

$$\frac{\sqrt{1}}{\sqrt{12}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{12}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{1}{2\sqrt{3}}$$

Rationalize the denominator of \frac{1}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{\sqrt{3}}{6}$$