Solve sqrt{12}+3sqrt{48}-2sqrt{27}

$$\sqrt { 12 } + 3 \sqrt { 48 } - 2 \sqrt { 27 }$$

Evaluate

$$8\sqrt{3}\approx 13.856406461$$

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}.

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

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}.

$$2\sqrt{3}+3\times 4\sqrt{3}-2\sqrt{27}$$

Multiply 3 and 4 to get 12.

$$2\sqrt{3}+12\sqrt{3}-2\sqrt{27}$$

Combine 2\sqrt{3} and 12\sqrt{3} to get 14\sqrt{3}.

$$14\sqrt{3}-2\sqrt{27}$$

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}.

$$14\sqrt{3}-2\times 3\sqrt{3}$$

Multiply -2 and 3 to get -6.

$$14\sqrt{3}-6\sqrt{3}$$

Combine 14\sqrt{3} and -6\sqrt{3} to get 8\sqrt{3}.

$$8\sqrt{3}$$