Solve 5sqrt{12}-6sqrt{27}+3sqrt{48}

$$5 \sqrt { 12 } - 6 \sqrt { 27 } + 3 \sqrt { 48 }$$

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}.

$$5\times 2\sqrt{3}-6\sqrt{27}+3\sqrt{48}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{3}-6\sqrt{27}+3\sqrt{48}$$

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}.

$$10\sqrt{3}-6\times 3\sqrt{3}+3\sqrt{48}$$

Multiply -6 and 3 to get -18.

$$10\sqrt{3}-18\sqrt{3}+3\sqrt{48}$$

Combine 10\sqrt{3} and -18\sqrt{3} to get -8\sqrt{3}.

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

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}.

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

Multiply 3 and 4 to get 12.

$$-8\sqrt{3}+12\sqrt{3}$$

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

$$4\sqrt{3}$$