Solve sqrt{75}-2sqrt{12}-sqrt{27}

$$\sqrt { 75 } - 2 \sqrt { 12 } - \sqrt { 27 }$$

Evaluate

$$-2\sqrt{3}\approx -3.464101615$$

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}.

$$5\sqrt{3}-2\sqrt{12}-\sqrt{27}$$

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}.

$$5\sqrt{3}-2\times 2\sqrt{3}-\sqrt{27}$$

Multiply -2 and 2 to get -4.

$$5\sqrt{3}-4\sqrt{3}-\sqrt{27}$$

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

$$\sqrt{3}-\sqrt{27}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

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

$$-2\sqrt{3}$$