Solve 1/2sqrt{12}-2sqrt{75}+sqrt{18}

$$1 / 2 \sqrt { 12 } - 2 \sqrt { 75 } + \sqrt { 18 }$$

Evaluate

$$3\left(\sqrt{2}-3\sqrt{3}\right)\approx -11.345816581$$

Solution Steps

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}.

$$\frac{1}{2}\times 2\sqrt{3}-2\sqrt{75}+\sqrt{18}$$

Cancel out 2 and 2.

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

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}.

$$\sqrt{3}-2\times 5\sqrt{3}+\sqrt{18}$$

Multiply -2 and 5 to get -10.

$$\sqrt{3}-10\sqrt{3}+\sqrt{18}$$

Combine \sqrt{3} and -10\sqrt{3} to get -9\sqrt{3}.

$$-9\sqrt{3}+\sqrt{18}$$

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}.

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

Factor

$$3 {(\sqrt{2} - 3 \sqrt{3})} = -11.345816581$$