A little trick for square roots (mental math)

Someone sent me this little mental math trick for square roots. I liked it, didn't know it before, so here goes:
I read your suggestion for calculating square root without a calculator. I teach Math for Elementary Teachers and developmental math courses (algebra) to adults. I feel that the focus should be on understanding the number rather than an exercise in following a memorized algorithm. I suggest you have the student determine the pair of perfect squares the number falls between. For example, if finding the sqrt of 645, it falls between the sqrt of 625 which equals 25 and the sqrt of 676 which equals 26. So the sqrt of 645 has to be between 25 and 26. Where does it fall between? There are 50 numbers between 676 and 625. 645 is 20 numbers beyond 625, so 20/50 = 0.4
So the sqrt of 645 is very close to 25.4
This method provides the student with a process that improves their understanding of numbers without expecting them to memorize an algorithm, and it provides an answer to the nearest tenth.

Andrea S. Levy, Ed.D.
She is referring to my article about the square root algorithm. However, I've never meant that kids would need to learn that long algorithm in school work. In the article, I'm actually advocating the method of finding the approximate square root by "guess and check".


vishal said…
hey maria i did not understand the trick properly can u help me out???

plz i am a student in india in std 10 in ICSE board

- vishal
Anonymous said…
Hi Maria,
It is a good effort from your part to find a strategy to get square root of numbers which are not square numbers. But it does take much of the needed time to go for other problems and the use of calculator rather would be more practical for such numbers.
Mr Sand (TIS)
Maria Miller said…
Of course calculator is what one would use, most of the time, for square roots. But the teacher could show this square root trick to students in order to help them learn better the actual concept of square root itself and to develop number sense.
Anonymous said…
I am taking the ASVAB tomorrow. Thank you for helping me understand square roots more clearly. I absolutely need to know math, especially since I am joining the Navy.
Jason Barnhard said…
This is a fantastic concept. I have been looking for a way to find square roots that is a little easier for the younger generation. the long division method is just too complicated with all its doubling and moving numbers. you definitely helped me out a lot.
Anonymous said…
i like it but, I like knowing te EXACT answer
Anonymous said…
625 minus 676 is 51 rather than the stated 50. 20/51 is. 39 and dead on for the sqrt(645), which everyone typed by now.

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