Solve sqrt{75}+3sqrt{18}-2sqrt{12}-2sqrt{50}

$$\sqrt { 75 } + 3 \sqrt { 18 } - 2 \sqrt { 12 } - 2 \sqrt { 50 }$$

Evaluate

$$\sqrt{3}-\sqrt{2}\approx 0.317837245$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$5\sqrt{3}+3\sqrt{18}-2\sqrt{12}-2\sqrt{50}$$

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}.

$$5\sqrt{3}+3\times 3\sqrt{2}-2\sqrt{12}-2\sqrt{50}$$

Multiply 3 and 3 to get 9.

$$5\sqrt{3}+9\sqrt{2}-2\sqrt{12}-2\sqrt{50}$$

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}.

$$5\sqrt{3}+9\sqrt{2}-2\times 2\sqrt{3}-2\sqrt{50}$$

Multiply -2 and 2 to get -4.

$$5\sqrt{3}+9\sqrt{2}-4\sqrt{3}-2\sqrt{50}$$

Combine 5\sqrt{3} and -4\sqrt{3} to get \sqrt{3}.

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

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}.

$$\sqrt{3}+9\sqrt{2}-2\times 5\sqrt{2}$$

Multiply -2 and 5 to get -10.

$$\sqrt{3}+9\sqrt{2}-10\sqrt{2}$$

Combine 9\sqrt{2} and -10\sqrt{2} to get -\sqrt{2}.

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