Solve (2sqrt{12}+4sqrt{18})+sqrt{3}=

$$( 2 \sqrt { 12 } + 4 \sqrt { 18 } ) + \sqrt { 3 } =$$

Evaluate

$$5\sqrt{3}+12\sqrt{2}\approx 25.630816786$$

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}.

$$2\times 2\sqrt{3}+4\sqrt{18}+\sqrt{3}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{3}+4\sqrt{18}+\sqrt{3}$$

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}.

$$4\sqrt{3}+4\times 3\sqrt{2}+\sqrt{3}$$

Multiply 4 and 3 to get 12.

$$4\sqrt{3}+12\sqrt{2}+\sqrt{3}$$

Combine 4\sqrt{3} and \sqrt{3} to get 5\sqrt{3}.

$$5\sqrt{3}+12\sqrt{2}$$