Solve 3sqrt{2}-2sqrt{18}+3sqrt{72}

$$3 \sqrt { 2 } - 2 \sqrt { 18 } + 3 \sqrt { 72 }$$

Evaluate

$$15\sqrt{2}\approx 21.213203436$$

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}.

$$3\sqrt{2}-2\times 3\sqrt{2}+3\sqrt{72}$$

Multiply -2 and 3 to get -6.

$$3\sqrt{2}-6\sqrt{2}+3\sqrt{72}$$

Combine 3\sqrt{2} and -6\sqrt{2} to get -3\sqrt{2}.

$$-3\sqrt{2}+3\sqrt{72}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

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

Multiply 3 and 6 to get 18.

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

Combine -3\sqrt{2} and 18\sqrt{2} to get 15\sqrt{2}.

$$15\sqrt{2}$$