Square Roots

Date: 08/19/2003 at 17:16:58
From: Emily
Subject: Square Roots

Why is a square root called a square root?

Date: 08/20/2003 at 13:02:31
From: Doctor Ian
Subject: Re: Square Roots

Hi Emily,

Suppose we have a square where we know each side has length 2:

      2
   +----+
   |    | 2
   |    |  
   +----+

The area of the square is given by 

  area = side * side

       = 2 * 2 

       = 4

Does that look familiar so far?  Okay, now what if someone gives us a
square, and tells us that the area is 9, and we want to know what the
length of a side is? 

      
   +----+                                    __
   |    |      9 = ? * ?      ==>      ? = \| 9 = 3
   |    |  
   +----+
      ?

In this case, we want to know what number we can multiply by itself to
get the area of the square, if we already know the area.  We call this
number the 'square root' of the area. 

In the same way, if we know the volume of a cube, but not the length
of a side, 

        
      +-----+
     /     /|  
    /     / |                                   ___
   +-----+  +                                 3|
   |     | /     64 = ? * ? * ?     ==>   ? = \| 64 = 4
   |     |/    
   +-----+
      ?

we take the 'cube root' of the volume to find the length of a side. 

Does this help? 

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