Solve sqrt{12}-sqrt{243}-sqrt{75}

$$\sqrt { 12 } - \sqrt { 243 } - \sqrt { 75 }$$

Evaluate

$$-12\sqrt{3}\approx -20.784609691$$

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}.

$$2\sqrt{3}-\sqrt{243}-\sqrt{75}$$

Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.

$$2\sqrt{3}-9\sqrt{3}-\sqrt{75}$$

Combine 2\sqrt{3} and -9\sqrt{3} to get -7\sqrt{3}.

$$-7\sqrt{3}-\sqrt{75}$$

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}.

$$-7\sqrt{3}-5\sqrt{3}$$

Combine -7\sqrt{3} and -5\sqrt{3} to get -12\sqrt{3}.

$$-12\sqrt{3}$$