Solve =sqrt{54}+3sqrt{96}

$$= \sqrt { 54 } + 3 \sqrt { 96 }$$

Evaluate

$$15\sqrt{6}\approx 36.742346142$$

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}.

$$3\sqrt{6}+3\sqrt{96}$$

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

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

Multiply 3 and 4 to get 12.

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

Combine 3\sqrt{6} and 12\sqrt{6} to get 15\sqrt{6}.

$$15\sqrt{6}$$