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

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

Evaluate

$$12\sqrt{2}+8-2\sqrt{6}-6\sqrt{3}\approx 9.679278417$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{2}+3 by each term of 4\sqrt{2}-2\sqrt{3}.

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

The square of \sqrt{2} is 2.

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

Multiply 4 and 2 to get 8.

$$8-2\sqrt{2}\sqrt{3}+12\sqrt{2}-6\sqrt{3}$$

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

$$8-2\sqrt{6}+12\sqrt{2}-6\sqrt{3}$$

Factor

$$2 {(6 \sqrt{2} + 4 - \sqrt{6} - 3 \sqrt{3})} = 9.679278417$$