Solve 3sqrt{18}-3sqrt{32}+6sqrt{50}=

$$3 \sqrt{ 18 } -3 \sqrt{ 32 } +6 \sqrt{ 50 } =$$

Evaluate

$$27\sqrt{2}\approx 38.183766184$$

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}.

$$3\times 3\sqrt{2}-3\sqrt{32}+6\sqrt{50}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{2}-3\sqrt{32}+6\sqrt{50}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$9\sqrt{2}-3\times 4\sqrt{2}+6\sqrt{50}$$

Multiply -3 and 4 to get -12.

$$9\sqrt{2}-12\sqrt{2}+6\sqrt{50}$$

Combine 9\sqrt{2} and -12\sqrt{2} to get -3\sqrt{2}.

$$-3\sqrt{2}+6\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$-3\sqrt{2}+6\times 5\sqrt{2}$$

Multiply 6 and 5 to get 30.

$$-3\sqrt{2}+30\sqrt{2}$$

Combine -3\sqrt{2} and 30\sqrt{2} to get 27\sqrt{2}.

$$27\sqrt{2}$$