Question

simply the square root of 4x^2y^4

Answer 1

2xy

Answer 2

So, first can you simplify \(\sqrt(x^2)\)

Answer 3

How about \(\sqrt(x^4)\)?

Answer 4

Be careful
\[
\sqrt { x^2} = |x|
\]

Answer 5

actually, it's + or -

Answer 6

\[
\sqrt{(-5)^2}=5 =|-5|

\]

Answer 7

Absolute value is not required
technically in front of every square root, there is a + or -

Answer 8

No sir

Answer 9

Yes, there is.

Answer 10

Look at the quadratic formula for reference

Answer 11

The square root is always positive or zero

Answer 12

Noooooo, How about \(\sqrt(-4)\)? That is neiither

Answer 13

A square root always has at least 2 possible answers provided the expression under the radical is not 0

Answer 14

Although, I would prefer to ask these to the poser of the question and not argue semantics on a basic problem.

Answer 15

I meant the function f(x) defined by
\[
f(x) = \sqrt x
\]
Has only one value which is the positive one. Otherwise it will not be a function.

Answer 16

Have Fun

Answer 17

Yes, in terms of functions, I agree. Thank you. You as well.

Answer 18

For me
\[
\sqrt{ 4x^2y^4}= 2 |x| y^2
\]

Answer 19

(function was not an initial condition here) Instead of the abs value I would put \[\left(\begin{matrix}+ \\ -\end{matrix}\right)2xy^2\] but like I said it's semantics in the long run.

Answer 20

We are arguing over the same answer, just written differently. A different approach

Answer 21

\[

\sqrt{ 4(-3)^2(2)^4}= 2 |-3| 2^2=2(3)(4)=24

\]

Answer 22

In that case, I disagree with your result.

Answer 23

The + is for x >0
The - for x <0
The |x| takes care of this distinction

Answer 24

I always keep the distinction

Answer 25

In this case I would have a -24. Due to the initial being a -3.

Answer 26

But nonetheless, I think it is a different approach. I have never seen your approach, though, I do understand why one would take it.