TO FIND SQUARE OF A 3 DIGIT NUMBER

LET THE NUMBER WHOSE SQUARE IS TO BE CALCULATED BE XYZ.

Sq(XYZ) is calculated like this

STEP 1. Last digit = last digit of SQ (Z)
STEP 2. Second Last Digit = 2*Y*Z +  carryover from STEP 1.
STEP 3. Third Last Digit 2*X*Z+ Sq(Y) +  carryover from STEP 2.
STEP 4. Fourth last digit is 2*X*Y +  carryover from STEP 3.
STEP 5. In the beginning of result will be Sq(X) + any carryover from Step 4.

EXAMPLE:

SQ (421)

STEP 1. Last digit = last digit of SQ (1) =1
STEP 2. Second Last Digit = 2*2*1 + any carryover from STEP 1= 4
STEP 3. Third Last Digit 2*4*1+ Square (2) + any carryover from STEP 2.= 2*4*1 +4= 12

  so 2 would be the third last digit  and 1 carryover
STEP 4. Fourth last digit is 2*4*2 + any carryover (which is 1)  = 16+1=17.

 So 7 and carry over 1.
STEP 5. In the beginning of result will be Sq (4) + any carryover from Step 4.

 So 16+1 =17.

So the result will be  177241.


Hope you enjoyed the concept.

Quant Concepts-Square of Numbers

Over the next few weeks , I will be covering some essential quantitative ability concepts which are a must for cracking the QA/DI section of CAT.

Let me start by explaining the concept of calculating squares of numbers.

Say , a number 312

312^2.

Determine the closest power of  100/10 as the case may be which is called the base.

In this case we obtain a base of 300.

represent 312^2 as (300+12)^2. here, deviation=12.

 Now,

 follow the step

ldigit(s) before 0 in base x  (number  + deviation) | deviation^2 where | is a separating  line separating 2 parts of calculation.

 

Remember ,

no. of digits on right side of the imaginary line should be exactly same as the no. of zeros in our base.

 

So, our problem boils down to:

3 x (312 + 12) | 12^2

3x324 | 144

972 | 144

= 97344....1 of 144 carried .

Another example:

38^2

base 30

3x(38 + 8 ) | 8x8

= 138 | 64

= 1444( as only digit should be on the right side of the imaginary line as base has one zero)

So,the 6 in the imaginary part is added to 138.

Comments are welcome and in case of doubts just leave a comment. I will cover them and other concepts in the next blog.

 

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