Solve (3sqrt{8})^2

$$( 3 \sqrt { 8 } ) ^ { 2 }$$

Evaluate

$$72$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Multiply 3 and 2 to get 6.

$$\left(6\sqrt{2}\right)^{2}$$

Expand \left(6\sqrt{2}\right)^{2}.

$$6^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$36\times 2$$

Multiply 36 and 2 to get 72.

$$72$$

Factor

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