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Base Method of Squaring a number:

Base method of squaring is very much easy and quick technique of Vedic mathematics. In this method we need to consider two types of base, which are

  • Actual base: 10, 100, 1000, 10000 and so on
  • Working base: 20, 30, 40, 200, 300, 400 etc. Working base taken by multiplying the actual base with integers. If we have to find square of 22 then the working base must be 20(10×2), but actual base is 10.

I know these things are little confusing, but don‟t worry after some example it will clear doubts about this method. Let us take some example:-

Example 1: Find the square of 24

Solution: Here actual base is 10, but we cannot take 10 as working base. We need to take 20 as working base since (10×2=20).

Since 24 is more than 20, so we need to add 4 to 24, and we get (24+4)=28, now since our working base is 20 and 20 is obtain by multiplying actual base which is 10 with 2, we need to multiply 28 with 2. So, (28×2) =56, and “56” will be the LHS of the final answer.

Now for RHS we need to find the square of 4 which is 16. Now here is the confusion is whether to put 16 or 6 in RHS. We need to put only “6” in RHS, because our actual base containing only one zero.

Remember, if actual base is 100 we need to put 2 digits in the RHS, if 1000 we put 3 digits in RHS. Now what happened to the “1” in 16. We simply add 1 to 56 in LHS. So, final answer is 576.

Example 2: Find square 296

Solution: Here actual base is 100 and working base is 300, since 296 is closer to 300 than 200. Step by step solution method is analyzed below,

  • 1 st of all find out how much less is 296 from 300, so 296 is 4 less from 300 so we need to subtract 4 from 296 which is 292.
  • Now multiply 292 with 3 since our actual base is multiply with 3 to get working base.
  • (292×3)=876, which will be our LHS.
  • Now for RHS we need two digit, since our actual base has two zero.
  • Squaring 4 we get the RHS, i.e. 16 is in RHS.
  • So our final answer is 87616.

Example 3: Find square of 104.

Solution: Here our actual base is also our working base, since 104 is closer to 100. Step by step detailed analysis is given below,

  • 1 st of all add 4 to 104 to get LHS which is 108, since 104 is more than 100 by 4.
  • Now for RHS square the number 4 and we get 16 as RHS.
  • So final answer is 10816.

Checklist:

1. Check for actual and working base, if actual base itself close to the
number takes it as working base.
2. Select the base which is closer to the number.
3. Put the digit equal to the number of zeros in actual base.
4. If we get 2 digit number of actual base 10 for RHS then adds the unit
place digit to the LHS. Same rule is applied for 100, 1000 base and
so on.