Solve sqrt{2}(sqrt{12}+sqrt{18}

$$\sqrt { 2 } ( \sqrt { 12 } + \sqrt { 18 }$$

Evaluate

$$2\left(\sqrt{6}+3\right)\approx 10.898979486$$

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}.

$$\sqrt{2}\left(2\sqrt{3}+\sqrt{18}\right)$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

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

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

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

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

The square of \sqrt{2} is 2.

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

Multiply 3 and 2 to get 6.

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