Stuck on a problem.

[Meku]

Hi! Today, I'm having trouble on my algebra problems. We are reviewing square roots and how to simplify them, even if they are irrational.
So today's homework problem was :

Order the numbers from least to greatest. Identify type of number -- whole, integer, rational, irrational.
-1/4 , 2√3 , -0.2 , 2√2 , √5.

The only thing I'm confused about is the numbers with the square root signs over them.
I have no idea how to compare them to the rest, and my teacher has not clarified how to revert them back to its original form.
So how can I compare those numbers?
(This is an emergency by the way, it is getting very late and the paper is due tomorrow.)

 

[Bob Brown MSEE]

Hint: If a list of POSITIVE numbers are in order, then their squared values will also be in order.

 

[Meku]

Hint: If a list of POSITIVE numbers are in order, then their squared values will also be in order.

Oh! Thank you very much. I'll try to work it out.

 

[stapel]

Order the numbers from least to greatest. Identify type of number -- whole, integer, rational, irrational.
-1/4 , 2√3 , -0.2 , 2√2 , √5.

The only thing I'm confused about is the numbers with the square root signs over them.
I have no idea how to compare them to the rest, and my teacher has not clarified how to revert them back to its original form.

What do you mean by "reverting them back to [their] original form"?

Also, are you allowed to plug these into a calculator, so you can compare their decimal approximations?

 

[Deleted member 4993]

You would not need to use a calculator - if you work with the hint by HoI, namely:

If a >1 and b>1 then a²>b² implies a>b

 

[lookagain]

You would not need to use a calculator - if you work with the hint by > > HoI, < < namely:

If a >1 and b>1 then a²>b² implies a>b

(The hint happened to be by Bob Brown MSEE in this case.)