Solve 2sqrt{12}+3sqrt{27}

$$2 \sqrt { 12 } + 3 \sqrt { 27 }$$

Evaluate

$$13\sqrt{3}\approx 22.516660498$$

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}.

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

Multiply 2 and 2 to get 4.

$$4\sqrt{3}+3\sqrt{27}$$

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}.

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

Multiply 3 and 3 to get 9.

$$4\sqrt{3}+9\sqrt{3}$$

Combine 4\sqrt{3} and 9\sqrt{3} to get 13\sqrt{3}.

$$13\sqrt{3}$$