Solve 4sqrt{12}+3sqrt{18}-sqrt{50}-2sqrt{48}

$$4 \sqrt { 12 } + 3 \sqrt { 18 } - \sqrt { 50 } - 2 \sqrt { 48 }$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

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}.

$$4\times 2\sqrt{3}+3\sqrt{18}-\sqrt{50}-2\sqrt{48}$$

Multiply 4 and 2 to get 8.

$$8\sqrt{3}+3\sqrt{18}-\sqrt{50}-2\sqrt{48}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$8\sqrt{3}+3\times 3\sqrt{2}-\sqrt{50}-2\sqrt{48}$$

Multiply 3 and 3 to get 9.

$$8\sqrt{3}+9\sqrt{2}-\sqrt{50}-2\sqrt{48}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$8\sqrt{3}+9\sqrt{2}-5\sqrt{2}-2\sqrt{48}$$

Combine 9\sqrt{2} and -5\sqrt{2} to get 4\sqrt{2}.

$$8\sqrt{3}+4\sqrt{2}-2\sqrt{48}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$8\sqrt{3}+4\sqrt{2}-2\times 4\sqrt{3}$$

Multiply -2 and 4 to get -8.

$$8\sqrt{3}+4\sqrt{2}-8\sqrt{3}$$

Combine 8\sqrt{3} and -8\sqrt{3} to get 0.

$$4\sqrt{2}$$