Multiplying a Number by Itself
Date: 02/27/2001 at 15:57:54 From: Justin Fleming Subject: Square roots You have adequately explained how you get a square root, and I understand that part of it. My question to you is so what? What does it mean to multiply a number by itself? I can understand the concept of adding or subtracting; that has meaning to me. It represents an order that I can understand in my daily life activities. But how did someone just say I am going to multiply this number by itself and call it a square root?
Date: 02/27/2001 at 22:52:02 From: Doctor Peterson Subject: Re: Square roots Hi, Justin. At first I thought you were saying the wrong thing in your last sentence, but I think you mean "If I take a number and multiply it by itself, I can call the original number the square root of the new number." That's correct, and I suppose I can see why you might think it's a little silly to go through all that. But it's really no different from what we do with addition and subtraction. I can add 6 to 3 and get 9; then I can subtract 6 from 9 and get back to my original number, 3. Subtraction is how we "undo" addition; and square roots are how we "undo" squaring. We don't subtract just to get back to a number we started with; rather, we usually subtract to find out what we would have had to start with, but didn't know. It's the same with square roots: we use them to find numbers we don't already have. You ask what squaring means. Squares arise in many problems; the simplest is the one from which it gets its name. If you make a square whose sides are all 5 inches long, then its area is 5x5 = 25 square inches. We've multiplied one side by the other to find how many one-inch squares it takes to cover it. So if we knew how many square inches we had (say, what area a gallon of paint covers), we could find the side of the square using a square root. Another example where the square root is important is the Pythagorean theorem. This says, for example, that if I have a 3x4 rectangle, I can find the square of the length of its diagonal by squaring the 3, squaring the 4, and adding the numbers together: 3^2 + 4^2 = 9 + 16 = 25. Now what is the length of the diagonal? The square root of this, which is 5. Without the square root, we couldn't solve this problem. I hope this helps you see the meaning and the value of the square root a little better. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.