Associated Topics || Dr. Math Home || Search Dr. Math

### 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/
```
Associated Topics:
Middle School Definitions
Middle School Terms/Units of Measurement

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search