Solve 5sqrt{6}+8sqrt{54}

$$5 \sqrt { 6 } + 8 \sqrt { 54 }$$

Evaluate

$$29\sqrt{6}\approx 71.035202541$$

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}.

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

Multiply 8 and 3 to get 24.

$$5\sqrt{6}+24\sqrt{6}$$

Combine 5\sqrt{6} and 24\sqrt{6} to get 29\sqrt{6}.

$$29\sqrt{6}$$