Square of any number by easy Vedic math’s trick
It is really a lengthy & complicated to find Square & Square-root of any number. Here we apply method which is very easy & fast to find the square of any number. This method is work like Base method of multiplication.
To find square of any number Vedic sutra 13 Sopaantyadvayamantyam is applicable.
Case 1: Number is near the power of 10 like 10,100,1000 etc.
Ex.i) 82
Here, Base = 10 (power of 10 number as base)
Difference = Number – Base
= 8-10 = -2
If we divide our answer in two parts as,
Answer = LHS/RHS
Put the values in formula
RHS = (-2)2 = 4
Note: Number of digit in RHS is equal to number of Zero in base. If less digit is there add 0 in left side of RHS & if number of digits are more then carryover to extra digit in LHS of the answer.
Put the values in formula,
LHS = 8+(-2) =6
Answer = 6/4 =64
Ex. ii) 932
Here, Base = 100 (As number is closed to 100)
Difference = 93-100 =-7
RHS = Difference2= (-7)2 = 49
LHS = Number + Difference
= 93 + (-7) = 86
Answer, 932 = 8649
Ex. iii) 9922
Here base = 1000
Difference = 992 – 1000 =- 008
Answer = (Number+Difference)/Difference2
= (992+(-008)) /(-008)2
= 984/064 (We add zero as base is 1000, so 3- digit should be there)
Answer, 9922 = 984064
Similarly,
Ex.iv)1122
Base = 100 & Difference = 112-100 = 12
Answer = (112 +12)/122
= 124/144 (As base is 100 so, only 2-digit in RHS & carryover 1)
Answer, 1122 = 12544
Case 2: Number is NOT near the power of 10 like 10,100,1000 etc.
If number is not near the 10, 100 1000 etc. in such case we consider 2- base one is Actual base & other is working base. Actual base is the base we used in above sum where as Working base is the number which is multiplier of 10 like 30,50,340,400,550 etc.
e.g. Number = 712
Here Actual base = 1000 (As number is close to 1000)
difference = 1000-712 = 288,
which is a big number & it is complicated to find difference2 . So, here we consider working base the number which is near the given example & also multiplier of the 10.
Here working base = 700.
Ex. v) 3922
Actual base = 100
Working base = 400 = 4 x Actual base
Difference = 392-400= (-08)
RHS = Diff.2=(-08)2=64
LHS = Num. + Diff. =392 + (-8) = 384
But working base = 4 x Actual base
So Actual LHS = 4 x LHS
= 4 x 384 =1536
Answer, 3922 =1536/64 = 153664
vi) 672 =
Actual base = 10
Working base = 70 = 7 x Actual base
Difference = 67-70= (-3)
RHS = Diff.2=(-3)2=9
LHS = Num. + Diff. =67 + (-3) = 64
But working base = 7 x Actual base
So Actual LHS = 7 x LHS
= 7 x 64 =448
Answer, 3922 =448/9 = 4489
Ex. vii) 5132
Actual base = 100
Working base = 500 = 5 x Actual base
Difference = 513-500= 13
RHS = Diff.2=(13)2=169
LHS = Num. + Diff. =513 + 13 = 526
But working base = 5 x Actual base
So Actual LHS = 5 x LHS
= 5 x 526 =2630
Answer, 5132 = 2630/169 (As base is 100 so, only 2- digit should be in RHS & carryover 1)
Answer, 5132 = 263169
Similarly,
Ex. viii) 382
Actual Base = 10
Working Base =40 =4 x 10
Answer =38+(-2) x 4/(-2)2
=36 x 4/4
Answer, 382 =1444
Ex. ix) 1032 Base = 100
103+03/32 =10609 (add 0 in RHS, as base is 100)
Ex. x) 1472
Actual Base = 100
Working Base =150 =(3/2) x 100
Answer = 147+(-3)x(3/2)/(-3)2
=144 x (3/2)/ 09
=21609
OR
Actual Base = 10
Working Base =150 =15 x 10
Answer = 147+(-3) x 15/(-3)2
=144 x 15/ 9
=21609
Square-root of perfect square
As most of the schools & colleges ask for square-root of perfect square number so we find same here. For imperfect number it is little bit complicated so, we will study it in advanced level.
First, we memorized the square of the number 1 to 10
By observing last digit of square, we form one more table.
After observing the above table we can conclude that in the column of last digit of square number 2,3,7 & 8 are absent. That means the number having last digit 2,3,7 & 8 are not a perfect square.
Now to simplify our calculation we convert our table 1 as:
By using above table, we can find out square root of number up to 10000.
Ex. i) Find the square root of 8464
Step 1: Check the last digit of given square.
Here last digit is 4 so, from table 2 the last digit of the square root will be 2 or 8.
Step 2: Check the approximate square-root from table 3
From Table 3 we can conclude that number 8464 is lies between
It means our square-root is lies in between 90 & 100.
Step 3: From step 1 we know that last digit of square-root is 2 or 8, so from step 1 & 2 we can say that answer will be 92 or 98.
Step 4: Observe that number 8464 is close to 8100 or 10,000.
Here it is close to smaller number 8100, so our answer is also smaller number i.e. 92. So our answer is 92.
Answer, Square-root of 8464 = 92.
Ex. ii) Find the square-root of 2209
Step 1: Check the last digit of given square.
Here last digit is 9 so, from table 2 the last digit of the square root will be 3 or 7.
Step 2: Check the approximate square-root from table 3
From Table 3 we can conclude that number 2209 is lies between
It means our answer is lies in between 40 & 50.
Step 3: From step 1 we know that last digit of square-root is 3 or 7, so from step 1 & 2 we can say that answer will be 43 or 47.
Step 4: Observe that number 2209 is close to 1600 or 2500.
Here it is close to bigger number 2500, so our answer is also bigger number i.e. 47.
Answer, Square-root of 2209 = 47.
Now to find the square -root of five digit number we need to memorized square of 11 to 20 & convert in to 10’s multiplier.
Ex iii) Find the square-root of 16129.
Step 1: As last digit of number is 9,
so last digit of answer will be 3 or 7 from table 2.
Step 2: Observe table 4 16129 is between the square of 120 & 130.
Step 3: From step 1 last digit of answer is 3 or 7 means
answer will be 123 or 127.
Step 4: 16129 is closer to 16900 means square root is also a bigger number, i.e. 127.
Answer, Square- root of 16129= 127.
Similarly,
Ex. iv) Square-root of 33856
From table 2 last digit of answer will be 4 or 6.
Answer is in between 180 & 190 from table 4.
Answer will be 184 or 186, from above 2 steps
From table 4 Number 33856 is close to 32400, which is smaller number
So, answer is also smaller number i.e. 184.
Answer, Square-root of 33856 = 184.
Ex. v) Square-root of 7225
From table 2 last digit of answer will be 5.
From table 4 answer is in between 6400 & 8100, so our answer will be in between 80 & 90 from table 4.
So, answer will be 85.
Answer, Square-root of 7225 = 85.
Try This:
i) 1072 ii)9892 iii) 1672 iv) 11202
Find the square-root of,
v)8649 vi)30,276 vii) 3136
Find the below link to study more:
1.Find the cube & cube-root of any number by just observing it
2. Easiest way to find the Square of number ends with 5.
Leave a Reply