Solve (4sqrt{2}-3)(sqrt{6}-3)

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

Evaluate

$$8\sqrt{3}+9-3\sqrt{6}-12\sqrt{2}\approx -1.462625516$$

Solution Steps

Apply the distributive property by multiplying each term of 4\sqrt{2}-3 by each term of \sqrt{6}-3.

$$4\sqrt{2}\sqrt{6}-12\sqrt{2}-3\sqrt{6}+9$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$4\sqrt{2}\sqrt{2}\sqrt{3}-12\sqrt{2}-3\sqrt{6}+9$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$4\times 2\sqrt{3}-12\sqrt{2}-3\sqrt{6}+9$$

Multiply 4 and 2 to get 8.

$$8\sqrt{3}-12\sqrt{2}-3\sqrt{6}+9$$