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

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

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}.

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

Multiply 2 and 5 to get 10.

$$10\sqrt{3}-3\sqrt{27}+\sqrt{3}$$

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}.

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

Multiply -3 and 3 to get -9.

$$10\sqrt{3}-9\sqrt{3}+\sqrt{3}$$

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

$$\sqrt{3}+\sqrt{3}$$

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

$$2\sqrt{3}$$