Solve sqrt{12}+3sqrt{27}-sqrt{48}

$$\sqrt{ 12 } +3 \sqrt{ 27 } - \sqrt{ 48 }$$

Evaluate

$$7\sqrt{3}\approx 12.124355653$$

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}.

$$2\sqrt{3}+3\sqrt{27}-\sqrt{48}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

Multiply 3 and 3 to get 9.

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

Combine 2\sqrt{3} and 9\sqrt{3} to get 11\sqrt{3}.

$$11\sqrt{3}-\sqrt{48}$$

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}.

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

Combine 11\sqrt{3} and -4\sqrt{3} to get 7\sqrt{3}.

$$7\sqrt{3}$$