Solve 4sqrt{3}+3sqrt{12}-2sqrt{27}=

$$4 \sqrt { 3 } + 3 \sqrt { 12 } - 2 \sqrt { 27 } =$$

Evaluate

$$4\sqrt{3}\approx 6.92820323$$

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}.

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

Multiply 3 and 2 to get 6.

$$4\sqrt{3}+6\sqrt{3}-2\sqrt{27}$$

Combine 4\sqrt{3} and 6\sqrt{3} to get 10\sqrt{3}.

$$10\sqrt{3}-2\sqrt{27}$$

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}.

$$10\sqrt{3}-2\times 3\sqrt{3}$$

Multiply -2 and 3 to get -6.

$$10\sqrt{3}-6\sqrt{3}$$

Combine 10\sqrt{3} and -6\sqrt{3} to get 4\sqrt{3}.

$$4\sqrt{3}$$