Solve -sqrt{27}+4sqrt{24}+5sqrt{27}=

$$- \sqrt { 27 } + 4 \sqrt { 24 } + 5 \sqrt { 27 } =$$

Evaluate

$$4\left(2\sqrt{6}+3\sqrt{3}\right)\approx 40.380527633$$

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}.

$$-3\sqrt{3}+4\sqrt{24}+5\sqrt{27}$$

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}.

$$-3\sqrt{3}+4\times 2\sqrt{6}+5\sqrt{27}$$

Multiply 4 and 2 to get 8.

$$-3\sqrt{3}+8\sqrt{6}+5\sqrt{27}$$

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}.

$$-3\sqrt{3}+8\sqrt{6}+5\times 3\sqrt{3}$$

Multiply 5 and 3 to get 15.

$$-3\sqrt{3}+8\sqrt{6}+15\sqrt{3}$$

Combine -3\sqrt{3} and 15\sqrt{3} to get 12\sqrt{3}.

$$12\sqrt{3}+8\sqrt{6}$$