Solve 1/3sqrt{27}+3/4sqrt{48}+1/2sqrt{12}

$$\frac{ 1 }{ 3 } \sqrt{ 27 } + \frac{ 3 }{ 4 } \sqrt{ 48 } + \frac{ 1 }{ 2 } \sqrt{ 12 }$$

Evaluate

$$5\sqrt{3}\approx 8.660254038$$

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}.

$$\frac{1}{3}\times 3\sqrt{3}+\frac{3}{4}\sqrt{48}+\frac{1}{2}\sqrt{12}$$

Cancel out 3 and 3.

$$\sqrt{3}+\frac{3}{4}\sqrt{48}+\frac{1}{2}\sqrt{12}$$

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}.

$$\sqrt{3}+\frac{3}{4}\times 4\sqrt{3}+\frac{1}{2}\sqrt{12}$$

Cancel out 4 and 4.

$$\sqrt{3}+3\sqrt{3}+\frac{1}{2}\sqrt{12}$$

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

$$4\sqrt{3}+\frac{1}{2}\sqrt{12}$$

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}.

$$4\sqrt{3}+\frac{1}{2}\times 2\sqrt{3}$$

Cancel out 2 and 2.

$$4\sqrt{3}+\sqrt{3}$$

Combine 4\sqrt{3} and \sqrt{3} to get 5\sqrt{3}.

$$5\sqrt{3}$$