Solve 3*sqrt{2}-5*sqrt{18}+sqrt{32}-sqrt{50}=

$$3 \cdot \sqrt { 2 } - 5 \cdot \sqrt { 18 } + \sqrt { 32 } - \sqrt { 50 } =$$

Evaluate

$$-13\sqrt{2}\approx -18.384776311$$

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}.

$$3\sqrt{2}-5\times 3\sqrt{2}+\sqrt{32}-\sqrt{50}$$

Multiply -5 and 3 to get -15.

$$3\sqrt{2}-15\sqrt{2}+\sqrt{32}-\sqrt{50}$$

Combine 3\sqrt{2} and -15\sqrt{2} to get -12\sqrt{2}.

$$-12\sqrt{2}+\sqrt{32}-\sqrt{50}$$

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}.

$$-12\sqrt{2}+4\sqrt{2}-\sqrt{50}$$

Combine -12\sqrt{2} and 4\sqrt{2} to get -8\sqrt{2}.

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

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}.

$$-8\sqrt{2}-5\sqrt{2}$$

Combine -8\sqrt{2} and -5\sqrt{2} to get -13\sqrt{2}.

$$-13\sqrt{2}$$