Solve 3*sqrt{12}-sqrt{27}+sqrt{75}=

$$3 \cdot \sqrt { 12 } - \sqrt { 27 } + \sqrt { 75 } =$$

Evaluate

$$8\sqrt{3}\approx 13.856406461$$

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}.

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

Multiply 3 and 2 to get 6.

$$6\sqrt{3}-\sqrt{27}+\sqrt{75}$$

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}.

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

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

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

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}.

$$3\sqrt{3}+5\sqrt{3}$$

Combine 3\sqrt{3} and 5\sqrt{3} to get 8\sqrt{3}.

$$8\sqrt{3}$$