Solve sqrt{12}(3sqrt{3}+1)

$$\sqrt { 12 } ( 3 \sqrt { 3 } + 1 )$$

Evaluate

$$2\left(\sqrt{3}+9\right)\approx 21.464101615$$

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}.

$$2\sqrt{3}\left(3\sqrt{3}+1\right)$$

Use the distributive property to multiply 2\sqrt{3} by 3\sqrt{3}+1.

$$6\left(\sqrt{3}\right)^{2}+2\sqrt{3}$$

The square of \sqrt{3} is 3.

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

Multiply 6 and 3 to get 18.

$$18+2\sqrt{3}$$