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

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

Evaluate

$$4\sqrt{3}\left(\sqrt{6}-1\right)\approx 10.042359518$$

Solution Steps

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}.

$$2\times 3\sqrt{2}-2\sqrt{12}+2\sqrt{18}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{2}-2\sqrt{12}+2\sqrt{18}$$

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}.

$$6\sqrt{2}-2\times 2\sqrt{3}+2\sqrt{18}$$

Multiply -2 and 2 to get -4.

$$6\sqrt{2}-4\sqrt{3}+2\sqrt{18}$$

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}.

$$6\sqrt{2}-4\sqrt{3}+2\times 3\sqrt{2}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{2}-4\sqrt{3}+6\sqrt{2}$$

Combine 6\sqrt{2} and 6\sqrt{2} to get 12\sqrt{2}.

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

Factor

$$4 \sqrt{3} {(\sqrt{2} \sqrt{3} - 1)} = 10.042359518$$