Solve 7sqrt{6}+5sqrt{54}

$$7 \sqrt { 6 } + 5 \sqrt { 54 }$$

Evaluate

$$22\sqrt{6}\approx 53.888774341$$

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}.

$$7\sqrt{6}+5\times 3\sqrt{6}$$

Multiply 5 and 3 to get 15.

$$7\sqrt{6}+15\sqrt{6}$$

Combine 7\sqrt{6} and 15\sqrt{6} to get 22\sqrt{6}.

$$22\sqrt{6}$$