Using the Ones Digit to Estimate Square RootsDate: 02/11/2005 at 11:56:25 From: Tina Subject: How to find square roots Dear Dr. Math, I am having trouble figuring out square roots quickly. For bigger numbers like 289, I have to try a lot of numbers before I get the answer. Usually, I square a number near 20, and see if the result is less or greater than the squared number. Then I try another number. Could you please help me? Sincerely, Tina Date: 02/11/2005 at 13:38:35 From: Doctor Ian Subject: Re: How to find square roots Hi Tina, Just looking at the units place can tell you a lot. For example, with 289, we have to multiply something so that the units digit squared ends in a 9. The only way for that to happen is for the units digit to be a 3 or a 7. So you just have to check 13 and 17. Similarly, suppose you want to find the square root of 256? The units digit is 6, which means the square root has to have a units digit of 4 or 6, so you only have to check 14 and 16. There aren't all that many possibilities for the units digit: _0^2 = _0 _1^2 = _1 _2^2 = _4 _3^2 = _9 _4^2 = _6 _5^2 = _5 _6^2 = _6 _7^2 = _9 _8^2 = _4 _9^2 = _1 So looking at it the other way, ___ \/ _0 = _0^2 ___ \/ _1 = _1^2 or _9^2 ___ \/ _4 = _2^2 or _8^2 ___ \/ _5 = _5^2 ___ \/ _6 = _4^2 or _6^2 ___ \/ _9 = _3^2 or _7^2 Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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