Solve 4sqrt{27}+32sqrt{12}-8sqrt{3}

$$4 \sqrt { 27 } + 32 \sqrt { 12 } - 8 \sqrt { 3 }$$

Evaluate

$$68\sqrt{3}\approx 117.779454915$$

Solution Steps

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}.

$$4\times 3\sqrt{3}+32\sqrt{12}-8\sqrt{3}$$

Multiply 4 and 3 to get 12.

$$12\sqrt{3}+32\sqrt{12}-8\sqrt{3}$$

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}.

$$12\sqrt{3}+32\times 2\sqrt{3}-8\sqrt{3}$$

Multiply 32 and 2 to get 64.

$$12\sqrt{3}+64\sqrt{3}-8\sqrt{3}$$

Combine 12\sqrt{3} and 64\sqrt{3} to get 76\sqrt{3}.

$$76\sqrt{3}-8\sqrt{3}$$

Combine 76\sqrt{3} and -8\sqrt{3} to get 68\sqrt{3}.

$$68\sqrt{3}$$