Solve (2sqrt{4}+sqrt{12})*(sqrt{12}-sqrt{4})-sqrt{44}

$$( 2 \sqrt { 4 } + \sqrt { 12 } ) \cdot ( \sqrt { 12 } - \sqrt { 4 } ) - \sqrt { 44 }$$

Evaluate

$$4\sqrt{3}+4-2\sqrt{11}\approx 4.29495365$$

Solution Steps

Calculate the square root of 4 and get 2.

$$\left(2\times 2+\sqrt{12}\right)\left(\sqrt{12}-\sqrt{4}\right)-\sqrt{44}$$

Multiply 2 and 2 to get 4.

$$\left(4+\sqrt{12}\right)\left(\sqrt{12}-\sqrt{4}\right)-\sqrt{44}$$

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}.

$$\left(4+2\sqrt{3}\right)\left(\sqrt{12}-\sqrt{4}\right)-\sqrt{44}$$

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}.

$$\left(4+2\sqrt{3}\right)\left(2\sqrt{3}-\sqrt{4}\right)-\sqrt{44}$$

Calculate the square root of 4 and get 2.

$$\left(4+2\sqrt{3}\right)\left(2\sqrt{3}-2\right)-\sqrt{44}$$

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

$$8\sqrt{3}-8+4\left(\sqrt{3}\right)^{2}-4\sqrt{3}-\sqrt{44}$$

The square of \sqrt{3} is 3.

$$8\sqrt{3}-8+4\times 3-4\sqrt{3}-\sqrt{44}$$

Multiply 4 and 3 to get 12.

$$8\sqrt{3}-8+12-4\sqrt{3}-\sqrt{44}$$

Add -8 and 12 to get 4.

$$8\sqrt{3}+4-4\sqrt{3}-\sqrt{44}$$

Combine 8\sqrt{3} and -4\sqrt{3} to get 4\sqrt{3}.

$$4\sqrt{3}+4-\sqrt{44}$$

Factor 44=2^{2}\times 11. Rewrite the square root of the product \sqrt{2^{2}\times 11} as the product of square roots \sqrt{2^{2}}\sqrt{11}. Take the square root of 2^{2}.

$$4\sqrt{3}+4-2\sqrt{11}$$