Simplify the expression. Do not assume the variables represent positive numbers.

Question

So my problem is this,

 

sqrt(4x^2)

 

the instructions are in the title.  I believe the answer is 2x but I am told this is wrong.  not sure how to solve the problem when not assuming the variables are positive.

Answer 1

Scott,

 

The initial expression x=1 results in the following:

√4(1)^2=2

For x=-1

√4(-1)^2=2

 

But for your simplified expression, if x=1

2(1)=2

For x=-1

2(-1)=-2 so these are not equivalent if x can be negative. 

 

To simplify this, the solution is the absolute value of 2x, written l2xl.

 

Brittany

Answer 2

The expression is simplified the same for x ≥ 0 or x < 0.

√(4x²)

√(2²x²)

√(2x)²

2x

 

You might inquire why this is wrong.