Solve (10sqrt{12})^2

$$( 10 \sqrt { 12 } ) ^ { 2 }$$

Evaluate

$$1200$$

Solution Steps

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}.

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

Multiply 10 and 2 to get 20.

$$\left(20\sqrt{3}\right)^{2}$$

Expand \left(20\sqrt{3}\right)^{2}.

$$20^{2}\left(\sqrt{3}\right)^{2}$$

Calculate 20 to the power of 2 and get 400.

$$400\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$400\times 3$$

Multiply 400 and 3 to get 1200.

$$1200$$

Factor

$$2^{4}\times 3\times 5^{2}$$