Solve left(sqrt{12}-4right)left(sqrt{6}+9right)

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

Evaluate

$$6\sqrt{2}+18\sqrt{3}-4\sqrt{6}-36\approx -6.135763061$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Apply the distributive property by multiplying each term of 2\sqrt{3}-4 by each term of \sqrt{6}+9.

$$2\sqrt{3}\sqrt{6}+18\sqrt{3}-4\sqrt{6}-36$$

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

$$2\sqrt{3}\sqrt{3}\sqrt{2}+18\sqrt{3}-4\sqrt{6}-36$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$2\times 3\sqrt{2}+18\sqrt{3}-4\sqrt{6}-36$$

Multiply 2 and 3 to get 6.

$$6\sqrt{2}+18\sqrt{3}-4\sqrt{6}-36$$