Solve [log_{3}(27*81)+sqrt{4*2}]

$$[ \log _ { 3 } ( 27 \times 81 ) + \sqrt { 4 \times 2 } ]$$

Evaluate

$$2\sqrt{2}+7\approx 9.828427125$$

Solution Steps

Multiply 27 and 81 to get 2187.

$$\log_{3}\left(2187\right)+\sqrt{4\times 2}$$

The base 3 logarithm of 2187 is 7.

$$7+\sqrt{4\times 2}$$

Multiply 4 and 2 to get 8.

$$7+\sqrt{8}$$

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

$$7+2\sqrt{2}$$