Solve sqrt{12}+sqrt{27}*sqrt{18}

$$\sqrt { 12 } + \sqrt { 27 } \times \sqrt { 18 }$$

Evaluate

$$2\sqrt{3}+9\sqrt{6}\approx 25.5095093$$

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}.

$$2\sqrt{3}+\sqrt{27}\sqrt{18}$$

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}.

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

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}.

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

Multiply 3 and 3 to get 9.

$$2\sqrt{3}+9\sqrt{3}\sqrt{2}$$

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

$$2\sqrt{3}+9\sqrt{6}$$