Solve sqrt{18}+2sqrt{32}-3sqrt{50}

$$\sqrt { 18 } + 2 \sqrt { 32 } - 3 \sqrt { 50 }$$

Evaluate

$$-4\sqrt{2}\approx -5.656854249$$

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}.

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

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}.

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

Multiply 2 and 4 to get 8.

$$3\sqrt{2}+8\sqrt{2}-3\sqrt{50}$$

Combine 3\sqrt{2} and 8\sqrt{2} to get 11\sqrt{2}.

$$11\sqrt{2}-3\sqrt{50}$$

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}.

$$11\sqrt{2}-3\times 5\sqrt{2}$$

Multiply -3 and 5 to get -15.

$$11\sqrt{2}-15\sqrt{2}$$

Combine 11\sqrt{2} and -15\sqrt{2} to get -4\sqrt{2}.

$$-4\sqrt{2}$$