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

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

Evaluate

$$2\sqrt{6}\approx 4.898979486$$

Solution Steps

Use the distributive property to multiply 2\sqrt{3} by \sqrt{2}-2\sqrt{3}.

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$2\sqrt{6}-4\left(\sqrt{3}\right)^{2}+\left(2\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$2\sqrt{6}-4\times 3+\left(2\sqrt{3}\right)^{2}$$

Multiply -4 and 3 to get -12.

$$2\sqrt{6}-12+\left(2\sqrt{3}\right)^{2}$$

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

$$2\sqrt{6}-12+2^{2}\left(\sqrt{3}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$2\sqrt{6}-12+4\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$2\sqrt{6}-12+4\times 3$$

Multiply 4 and 3 to get 12.

$$2\sqrt{6}-12+12$$

Add -12 and 12 to get 0.

$$2\sqrt{6}$$