Solve sqrt{48}+2sqrt{3}-sqrt{27}

$$\sqrt{ 48 } +2 \sqrt{ 3 } - \sqrt{ 27 }$$

Evaluate

$$3\sqrt{3}\approx 5.196152423$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$4\sqrt{3}+2\sqrt{3}-\sqrt{27}$$

Combine 4\sqrt{3} and 2\sqrt{3} to get 6\sqrt{3}.

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

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}.

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

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

$$3\sqrt{3}$$