Metres Squared and Square Metres

Date: 05/02/2003 at 07:38:55
From: Nigel Knowles
Subject: Metres Squared and square metres

In

   Meters Squared vs. Square Meters
   http://mathforum.org/library/drmath/view/57209.html 

you have said that square metres and metres squared are the same 
thing, but this cannot be the case. 

If I have an square area of 5m x 5m this is actually termed 25 square 
metres.  But you state this can also be called 25 metres squared. But 
surely 25 metres squared is 25m x 25m, which is 625 square metres?

How do I write either of these down to avoid confusion?

Date: 05/02/2003 at 08:16:31
From: Doctor Ian
Subject: Re: Metres Squared and square metres

Hi Nigel, 

When we say 

  25 m^2

we mean 

  25 (m^2)

That is, following the conventional order of operations, we evaluate
the exponent first, so it applies only to the units. That's different
from

  (25 m)^2 = 25^2 m^2

Consider the expression

  5 + 3x^2

You don't interpret that as (3x)^2, right? Same thing here. 

> How do I write either of these down to avoid confusion?

You have to be careful about where you put the exponent. If you put
it on the quantity, it means to square the quantity, leaving the units
alone. If you put it on the units, it means to square the units,
leaving the quantity alone. If you want to square both, you have to
use parentheses to extend the scope of the exponent:

  25^2 m = (25*25) (m)

  25 m^2 = (25) (m*m)

  (25 m)^2 = (25*25) (m*m)

Does this help?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/