Final answer:
The square root of 54 over the square root of 6 simplifies to 3, by dividing 54 by 6 to get 9, and recognizing that the square root of 9 is 3.
Step-by-step explanation:
To simplify the square root of 54 over the square root of 6, we can start by expressing the square roots as fractional exponents and using exponent rules. First, let's rewrite the square roots as follows:
√54 = 54^(1/2), and √6 = 6^(1/2).
Next, we divide:
(54^(1/2)) / (6^(1/2)) = (54/6)^(1/2)
We find that 54 divided by 6 equals 9, giving us
9^(1/2)
Now, we recognize that the square root of 9 is 3 because 3 * 3 equals 9. So, the final answer simplifies to 3.