Solve 5sqrt{3}-sqrt{27}+4sqrt{48}

$$5 \sqrt { 3 } - \sqrt { 27 } + 4 \sqrt { 48 }$$

Evaluate

$$18\sqrt{3}\approx 31.176914536$$

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}.

$$5\sqrt{3}-3\sqrt{3}+4\sqrt{48}$$

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

$$2\sqrt{3}+4\sqrt{48}$$

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}.

$$2\sqrt{3}+4\times 4\sqrt{3}$$

Multiply 4 and 4 to get 16.

$$2\sqrt{3}+16\sqrt{3}$$

Combine 2\sqrt{3} and 16\sqrt{3} to get 18\sqrt{3}.

$$18\sqrt{3}$$