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

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

Evaluate

$$5\sqrt{2}-8\sqrt{3}\approx -6.785338649$$

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}.

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

Multiply 2 and 2 to get 4.

$$4\sqrt{3}-3\sqrt{48}+\sqrt{50}$$

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}.

$$4\sqrt{3}-3\times 4\sqrt{3}+\sqrt{50}$$

Multiply -3 and 4 to get -12.

$$4\sqrt{3}-12\sqrt{3}+\sqrt{50}$$

Combine 4\sqrt{3} and -12\sqrt{3} to get -8\sqrt{3}.

$$-8\sqrt{3}+\sqrt{50}$$

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}.

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