Question

For the expression \(\sqrt{a^2b^3}\) defined over the set of Real numbers, and ab ≠ 0, which of the following is not a factor of its simplified form?
A) a
B) |a|
C) b
D) \(\sqrt{b}\)
E) NOTA
I'm thinking B?

Answer 1

I think my answer would be B as well.

Answer 2

Ok. Thank you :)

Answer 3

You're welcome.

Answer 4

Turns out the answer is A?

Answer 5

If that's the case, I don't see why C wouldn't also be correct....

Answer 6

Wait, I think I have the solution explanation somewhere...hold on...

Answer 7

Interesting. I'll have to remember these little tricks in the future.

Answer 8

Alright. I'm not quite understanding how it's A though. Can you explain it? Like I know that b has to be positive and that a can be positive or negative, but I don't understand the rest...

Answer 9

Well, suppose \(a\) is negative, and suppose we factored as such\[\sqrt{a^2b^3}=ab\sqrt b\]Since \(a\) is negative, \(ab\sqrt{b}\) is negative as well. However, \(\sqrt{a^2b^3}\) is a positive number. Therefore\[\sqrt{a^2b^3}\neq ab\sqrt b\]And instead, we must take the absolute value of \(a\).

Answer 10

We conclude that it factors as\[\sqrt{a^2b^3}=|a|b\sqrt b\]

Answer 11

Then, if the factor is |a|, then how is it just 'a' by itself?

Answer 12

The question is asking: "Which of these is not a factor?" From our factorization, we see that \(a\) is not a factor.

Answer 13

Oh! Not a factor...I would've picked something else if I had read the correctly...I thought it said which IS a factor...thanks again :)

Answer 14

You're welcome :)