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

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

Evaluate

$$9\sqrt{3}\approx 15.588457268$$

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}.

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

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

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

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}.

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

Multiply 2 and 5 to get 10.

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

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

$$9\sqrt{3}$$