Solve 2sqrt{54}-3sqrt{27}+3sqrt{3}

$$2 \sqrt { 54 } - 3 \sqrt { 27 } + 3 \sqrt { 3 }$$

Evaluate

$$6\sqrt{6}-6\sqrt{3}\approx 4.304633611$$

Solution Steps

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$2\times 3\sqrt{6}-3\sqrt{27}+3\sqrt{3}$$

Multiply 2 and 3 to get 6.

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

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}.

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

Multiply -3 and 3 to get -9.

$$6\sqrt{6}-9\sqrt{3}+3\sqrt{3}$$

Combine -9\sqrt{3} and 3\sqrt{3} to get -6\sqrt{3}.

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