Question

Which of the following is equivalent to the quotient below?

√(135 ÷ √3)
A. 15√3
B. 27
C. 15
D. 9√3

Answer 1

The expression √(135 ÷ √3) simplifies initially as 1351/2/31/2. After simplifying, it becomes (135/3)1/2, which then results in 3√5. Unfortunately, this result does not match any of the provided answer choices.

Step-by-step explanation:

To find the equivalent of √(135 ÷ √3), we simplify the expression step by step:

1. We can rewrite √3 in the denominator as 3 to the power of 1/2 making the expression √135/31/2.
2. Given that √(x) is the same as x1/2, we have √135 as 1351/2, thus the expression becomes 1351/2/31/2.
3. Using the properties of exponents, we combine the terms to get (135/3)1/2.
4. 135 divided by 3 is equal to 45, so we now have 451/2, which is √45.
5. 45 can be factored into 9 * 5, and since 9 is a perfect square, we can take the square root of 9 to get 3. So, √45 becomes √(9*5) which simplifies to 3√5.
6. Finally, since 5 is not a perfect square, it cannot be simplified further and the expression remains as 3√5.

However, none of the answer choices A. 15√3, B. 27, C. 15, or D. 9√3 are equivalent to 3√5. Therefore, there might be a mistake in the simplification process, or the provided answers do not match the simplified quotient of the given expression.