Solve 3sqrt{24}+3sqrt{54}-2sqrt{2}

$$3 \sqrt { 24 } + 3 \sqrt { 54 } - 2 \sqrt { 2 }$$

Evaluate

$$15\sqrt{6}-2\sqrt{2}\approx 33.913919017$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$3\times 2\sqrt{6}+3\sqrt{54}-2\sqrt{2}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{6}+3\sqrt{54}-2\sqrt{2}$$

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}.

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

Multiply 3 and 3 to get 9.

$$6\sqrt{6}+9\sqrt{6}-2\sqrt{2}$$

Combine 6\sqrt{6} and 9\sqrt{6} to get 15\sqrt{6}.

$$15\sqrt{6}-2\sqrt{2}$$