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Application of Squaring integers ending in five

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Application of Squaring integers ending in five

by sirjon » Sun Aug 22, 2010 3:20 am
I wish to share one important use of what I call "middle square values" Also see: https://www.beatthegmat.com/mba/2010/08/ ... nding-in-5

Although I'm personally using this technique for quite a while now, I realized that getting the squares of two-digit numbers ending in 5, are also very useful in determining the location of the 'true square root' within a given set of possible square roots, see https://easysqrtsforkids.blocked/20 ... dging.html

Squaring integers ending in 5 is also very useful in SE MSM-2 format... the 'Grouping' Method in dealing with perfect square numbers ending in 25...

What do you think, 'common' with the squares of 15, 35, 65 and 85? how about the squares of 45, 55 and 95? lastly, common with the squares of 25 and 75?
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by sirjon » Thu Aug 26, 2010 10:23 pm
DEALING WITH SQUARES OF FIVE


Table of Multiples of Five Squares (M5.Sq)


05^2 = 0'25

15^2 = 2'25

25^2 = 6'25

35^2 = 12'25

45^2 = 20'25

55^2 = 30'25

65^2 = 42'25

75^2 = 56'25

85^2 = 72'25

95^2 = 90'25


If you look at the table above, you may notice that there are some "common things" about these following groups;


Group 1

15^2 = 2'25
35^2 = 12'25
65^2 = 42'25
85^2 = 72'25


Group 2

05^2 = 0'25 (sometimes, not included)
45^2 = 20'25
55^2 = 30'25
95^2 = 90'25


Group 3

25^2 = 6'25
75^2 = 56'25


Take Note:


1) The squares of 15, 35, 65 and 85, all end up with ...225


2) The squares of 5, 45, 55 and 95, all end up with ...025


3) The square of 25 and 75, end up with ...6'25


Always remember that all squares of numbers having a last digit of 5, will all, end up with ...25.

But the underlined numbers (2, 0 and 6), will give us a 'hint' of what the missing digits might be.

Check this out:

https://newsqroot.blocked/2010/08/n ... false.html
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