Question

Rewrite each expression without absolute value bars.

|sqrt2 - 5|

I have the answer, but I have no idea how we get there or why. I would appreciate an explanation :)

Answer 1

The problem is

\[\Large \left|\sqrt{2}-5\right|\]

correct?

Answer 2

Yes.

Answer 3

Since 2^2 = 4, this means that the square root of 2 is less than 5

So

\[\Large \sqrt{2} < 5\]

----------------

This means that

\[\Large \sqrt{2} < 5\]

\[\Large \sqrt{2} - 5 < 0\]

Answer 4

Now use the idea that

|x| = x ... if x >= 0

or

|x| = -x .... if x < 0