Solve sqrt{54}+sqrt{384}

$$\sqrt { 54 } + \sqrt { 384 }$$

Evaluate

$$11\sqrt{6}\approx 26.944387171$$

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}.

$$3\sqrt{6}+\sqrt{384}$$

Factor 384=8^{2}\times 6. Rewrite the square root of the product \sqrt{8^{2}\times 6} as the product of square roots \sqrt{8^{2}}\sqrt{6}. Take the square root of 8^{2}.

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

Combine 3\sqrt{6} and 8\sqrt{6} to get 11\sqrt{6}.

$$11\sqrt{6}$$