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

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

Evaluate

$$\sqrt{6}\approx 2.449489743$$

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}.

$$-3\sqrt{6}+2\sqrt{24}$$

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}.

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

Multiply 2 and 2 to get 4.

$$-3\sqrt{6}+4\sqrt{6}$$

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

$$\sqrt{6}$$