Solve sqrt{12}+2sqrt{27}

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

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}.

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

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}.

$$2\sqrt{3}+2\times 3\sqrt{3}$$

Multiply 2 and 3 to get 6.

$$2\sqrt{3}+6\sqrt{3}$$

Combine 2\sqrt{3} and 6\sqrt{3} to get 8\sqrt{3}.

$$8\sqrt{3}$$