Date: 07/17/98 at 12:54:28 From: Ted Subject: Problem Dear Dr.Math, My dad taught me how to do decimals, but now I am confused - what are square roots and what do they look like? Can you tell me?
Date: 07/17/98 at 16:46:49 From: Doctor Pat Subject: Re: Problem Ted, A square root is a simple idea, but some of them are hard to express in decimal form. First, to answer the question about what they are. If you multiply a number by itself, the answer is called the square of the number. For example, since 5x5 = 25 we call 25 the SQUARE of 5. In the same way 36 is the square of 6, etc. This probably came about because the area of a square with sides of 6 units is 36 square units. Now to work the other way, to find out what number times itself = 49 for instance, is called finding the square root. SOOOOOOOO the SQUARE ROOT of 25 is 5 because 5 SQUARED is 25; and the square root of 49 is 7, etc. So far so good, but sometimes it doesn't come out so nicely. For instance, what is the square root of 5? Well, it must be MORE than 2 because 2 is the square root of 4, and it must be LESS than 3 because 3 is the square root of 9, and 5 is between 4 and 9, so its square root must be between 2 and 3. We can guess 2.5 and see if that works. It's easy to test since we know we are right if 2.5 x 2.5 is equal to 5. Yikes, I got 6.25 which is too much, so we'd better guess a little lower. I could continue guessing and getting closer and closer to the answer, but I could NEVER get it exactly because it does not end and it does not repeat. Numbers like this are called irrational (which means NOT a fraction) because there is NO fraction of whole numbers that is exactly the same). A CLOSE answer for the square root of 5 is 2.236067977.... , my calculator ran out of digits, but that is still not EXACTLY right. I think there is a lot of new language here and you may need some time to think about all this. After you have spent some time on the square roots that have whole number answers, you can search the Dr. Math archives for other information on irrational numbers; there are a lot of them (actually an infinite number). Good luck, - Doctor Pat, The Math Forum http://mathforum.org/dr.math/
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