Solve sqrt{75}-2sqrt{27}-sqrt{3}

$$\sqrt { 75 } - 2 \sqrt { 27 } - \sqrt { 3 }$$

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}.

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

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}.

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

Multiply -2 and 3 to get -6.

$$5\sqrt{3}-6\sqrt{3}-\sqrt{3}$$

Combine 5\sqrt{3} and -6\sqrt{3} to get -\sqrt{3}.

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

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

$$-2\sqrt{3}$$