Solve (2sqrt{2}-4)^2+3sqrt{2}2

$$( 2 \sqrt { 2 } - 4 ) ^ { 2 } + 3 \sqrt { 2 } 2$$

Evaluate

$$24-10\sqrt{2}\approx 9.857864376$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2\sqrt{2}-4\right)^{2}.

$$4\left(\sqrt{2}\right)^{2}-16\sqrt{2}+16+2\times 3\sqrt{2}$$

The square of \sqrt{2} is 2.

$$4\times 2-16\sqrt{2}+16+2\times 3\sqrt{2}$$

Multiply 4 and 2 to get 8.

$$8-16\sqrt{2}+16+2\times 3\sqrt{2}$$

Add 8 and 16 to get 24.

$$24-16\sqrt{2}+2\times 3\sqrt{2}$$

Multiply 2 and 3 to get 6.

$$24-16\sqrt{2}+6\sqrt{2}$$

Combine -16\sqrt{2} and 6\sqrt{2} to get -10\sqrt{2}.

$$24-10\sqrt{2}$$

Factor

$$2 {(12 - 5 \sqrt{2})} = 9.857864376$$