Solve 2sqrt{27}+sqrt{75}-5sqrt{12}

$$2 \sqrt { 27 } + \sqrt { 75 } - 5 \sqrt { 12 }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

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}.

$$2\times 3\sqrt{3}+\sqrt{75}-5\sqrt{12}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{3}+\sqrt{75}-5\sqrt{12}$$

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}.

$$6\sqrt{3}+5\sqrt{3}-5\sqrt{12}$$

Combine 6\sqrt{3} and 5\sqrt{3} to get 11\sqrt{3}.

$$11\sqrt{3}-5\sqrt{12}$$

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}.

$$11\sqrt{3}-5\times 2\sqrt{3}$$

Multiply -5 and 2 to get -10.

$$11\sqrt{3}-10\sqrt{3}$$

Combine 11\sqrt{3} and -10\sqrt{3} to get \sqrt{3}.

$$\sqrt{3}$$