Solve 12^2:(-sqrt{5})^2:(sqrt{3})^2*sqrt{2^2}

$$12 ^ { 2 } : ( - \sqrt { 5 } ) ^ { 2 } : ( \sqrt { 3 } ) ^ { 2 } \times \sqrt { 2 ^ { 2 } }$$

Evaluate

$$\frac{96}{5}=19.2$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\frac{\frac{144}{\left(-\sqrt{5}\right)^{2}}}{\left(\sqrt{3}\right)^{2}}\sqrt{2^{2}}$$

Calculate -\sqrt{5} to the power of 2 and get \left(\sqrt{5}\right)^{2}.

$$\frac{\frac{144}{\left(\sqrt{5}\right)^{2}}}{\left(\sqrt{3}\right)^{2}}\sqrt{2^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\frac{144}{5}}{\left(\sqrt{3}\right)^{2}}\sqrt{2^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{144}{5}}{3}\sqrt{2^{2}}$$

Express \frac{\frac{144}{5}}{3} as a single fraction.

$$\frac{144}{5\times 3}\sqrt{2^{2}}$$

Multiply 5 and 3 to get 15.

$$\frac{144}{15}\sqrt{2^{2}}$$

Reduce the fraction \frac{144}{15} to lowest terms by extracting and canceling out 3.

$$\frac{48}{5}\sqrt{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{48}{5}\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$\frac{48}{5}\times 2$$

Multiply \frac{48}{5} and 2 to get \frac{96}{5}.

$$\frac{96}{5}$$

Factor

$$\frac{2 ^ {5} \cdot 3}{5} = 19\frac{1}{5} = 19.2$$