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

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

Evaluate

$$4\sqrt{3}+25-6\sqrt{6}-12\sqrt{2}\approx 0.260702025$$

Solution Steps

Square 3\sqrt{2}-2-\sqrt{3}.

$$-6\sqrt{2}\sqrt{3}+9\left(\sqrt{2}\right)^{2}+\left(\sqrt{3}\right)^{2}-12\sqrt{2}+4\sqrt{3}+4$$

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

$$-6\sqrt{6}+9\left(\sqrt{2}\right)^{2}+\left(\sqrt{3}\right)^{2}-12\sqrt{2}+4\sqrt{3}+4$$

The square of \sqrt{2} is 2.

$$-6\sqrt{6}+9\times 2+\left(\sqrt{3}\right)^{2}-12\sqrt{2}+4\sqrt{3}+4$$

Multiply 9 and 2 to get 18.

$$-6\sqrt{6}+18+\left(\sqrt{3}\right)^{2}-12\sqrt{2}+4\sqrt{3}+4$$

The square of \sqrt{3} is 3.

$$-6\sqrt{6}+18+3-12\sqrt{2}+4\sqrt{3}+4$$

Add 18 and 3 to get 21.

$$-6\sqrt{6}+21-12\sqrt{2}+4\sqrt{3}+4$$

Add 21 and 4 to get 25.

$$-6\sqrt{6}+25-12\sqrt{2}+4\sqrt{3}$$

Expand

$$4 \sqrt{3} + 25 - 6 \sqrt{6} - 12 \sqrt{2} = 0.260702025$$

Solution Steps

Square 3\sqrt{2}-2-\sqrt{3}.

$$-6\sqrt{2}\sqrt{3}+9\left(\sqrt{2}\right)^{2}+\left(\sqrt{3}\right)^{2}-12\sqrt{2}+4\sqrt{3}+4$$

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

$$-6\sqrt{6}+9\left(\sqrt{2}\right)^{2}+\left(\sqrt{3}\right)^{2}-12\sqrt{2}+4\sqrt{3}+4$$

The square of \sqrt{2} is 2.

$$-6\sqrt{6}+9\times 2+\left(\sqrt{3}\right)^{2}-12\sqrt{2}+4\sqrt{3}+4$$

Multiply 9 and 2 to get 18.

$$-6\sqrt{6}+18+\left(\sqrt{3}\right)^{2}-12\sqrt{2}+4\sqrt{3}+4$$

The square of \sqrt{3} is 3.

$$-6\sqrt{6}+18+3-12\sqrt{2}+4\sqrt{3}+4$$

Add 18 and 3 to get 21.

$$-6\sqrt{6}+21-12\sqrt{2}+4\sqrt{3}+4$$

Add 21 and 4 to get 25.

$$-6\sqrt{6}+25-12\sqrt{2}+4\sqrt{3}$$