Question

(1 point) Assume that x and y represent positive real numbers. Using the distributive

property to help simplify the expression
2√16xy-√16xy + 3√81xy
into the simplest radical form AVC, where A and C are either integers or
monomials.
Answer: A =
and C=

Answer 1

To simplify the expression 2√16xy - √16xy + 3√81xy, we can use the distributive property and simplify each term separately.

First, let's simplify the terms involving the square root of 16xy:

2√16xy - √16xy

The square root of 16 is 4, so we can rewrite this as:

2(4√xy) - 1(4√xy)

Simplifying further:

8√xy - 4√xy

Now, let's simplify the term involving the square root of 81xy:

3√81xy

The square root of 81 is 9, so we can rewrite this as:

3(9√xy)

Simplifying further:

27√xy

Now, let's combine the simplified terms:

(8√xy - 4√xy) + 27√xy

The terms 8√xy and -4√xy cancel each other out, leaving us with:

27√xy

Therefore, the simplified expression is 27√xy.

In terms of A and C, we have A = 27 and C = √xy.

So, the simplest radical form of the expression 2√16xy - √16xy + 3√81xy is 27√xy, where A = 27 and C = √xy.