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Re: SQUARE of any two digit number - shortcut
[#permalink]
11 Jun 2011, 09:29
1
Kudos
Expert Reply
arryputtar wrote:
29^2 how to solve this ?
Step 1: Identify the digits
29 - lets say "2" as "a" and "9" as b So 2-> a and 9-> b
Step 2: Plug into the equation below a^2 | 2(a*b) | b^2
instead of a -> use 2 and instead of b-> use 9
Step 3:
So by plugging in we get 2^2 | 2(2*9) | 9^2
Step 4: solve the thing
2^2 => 4 2(2*9) => 36 9^2 => 81
4 | 36 | 81
Step 5: this is the kewlest thing....all you need to do is carry over from right to left
4| 36 | 81 -> carry over 8 (left most digit just like addition) 4| 36 + 8 | 1 => 44 | 1 now from 44 carry over 4 4 + 4 | 4 | 1
8 | 4 |1 => 29 ^ 2 => 841
Fortunately we rarely (probably never) need to square awkward large numbers on the GMAT. If I need to find the value of 29^2, I'd take advantage of the difference of squares:
29^2 - 1 = (29 + 1)(29 -1) = (30)(28) = 840
so 29^2 = 841.
This would be a fast approach for a number ending in 9 or 1; for other numbers it would still lead to an awkward calculation.
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gmatclubot
Re: SQUARE of any two digit number - shortcut [#permalink]