Solve sqrt{12}+5sqrt{3}-sqrt{27}

$$\sqrt { 12 } + 5 \sqrt { 3 } - \sqrt { 27 }$$

Evaluate

$$4\sqrt{3}\approx 6.92820323$$

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}.

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

Combine 2\sqrt{3} and 5\sqrt{3} to get 7\sqrt{3}.

$$7\sqrt{3}-\sqrt{27}$$

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}.

$$7\sqrt{3}-3\sqrt{3}$$

Combine 7\sqrt{3} and -3\sqrt{3} to get 4\sqrt{3}.

$$4\sqrt{3}$$