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

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

Evaluate

$$9$$

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}.

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

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

$$3\sqrt{3}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3\times 3$$

Multiply 3 and 3 to get 9.

$$9$$

Factor

$$3^{2}$$