Solve (3sqrt{8})^2+3^2

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

Evaluate

$$81$$

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}.

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

Multiply 3 and 2 to get 6.

$$\left(6\sqrt{2}\right)^{2}+3^{2}$$

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

$$6^{2}\left(\sqrt{2}\right)^{2}+3^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36\left(\sqrt{2}\right)^{2}+3^{2}$$

The square of \sqrt{2} is 2.

$$36\times 2+3^{2}$$

Multiply 36 and 2 to get 72.

$$72+3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$72+9$$

Add 72 and 9 to get 81.

$$81$$

Factor

$$3^{4}$$