Shortcut to find Square Root of any Number
In every competitive exam, there is at least one instance where you will have to find the square root of a number quickly. With the help of this shortcut on how to find the square root of a number, you will be able to find out the square root of any number within seconds. This method is applicable only for perfect squares. Square root questions asked in competitive exams/bank exams are usually perfect squares. Refer How to check if a number is a perfect square? to find out if a given number is a perfect square.
Steps to Find the Square Root of a Number
Step 1: First of all group the number in pairs of 2 starting from the right.
Step2: To get the ten’s place digit, Find the nearest square (equivalent or greater than or less than) to the first grouped pair from left and put the square root of the square.
Step 3: To get the unit’s place digit of the square root
Remember the following
If the number ends in

Unit’s place digit of the square root

1

1 or 9(101)

4

2 or 8(102)

9

3 or 7(103)

6

4or 6(104)

5

5

0

0

Let’s see the logic behind this method to find square root for a better understanding
We know,
1^{2}=1
2^{2}=4
3^{2}=9
4^{2}=16
5^{2}=25
6^{2}=36
7^{2}=49
8^{2}=64
9^{2}=81
10^{2}=100
Now, observe the unit’s place digit of all the squares.
Do you find anything common?
We notice that,
Unit’s place digit of both 1^{2}and 9^{2 }is 1.
Unit’s place digit of both 2^{2} and 8^{2} is 4
And Unit’s place digit of both 3^{2} and 7^{2} is 9
Unit’s place digit of both 4^{2} and 6^{2} is 6.
Step 4: Multiply the ten’s place digit (found in step 1) with its consecutive number and compare the result obtained with the first pair of the original number from left.
Remember,
If the first pair of the original number > Result obtained on multiplication then select the greater number out of the two numbers as the unit’s place digit of the square root.
If the first pair of the original number < the result obtained on multiplication, then select the lesser number out of the two numbers as the unit’s place digit of the square root.
Let us consider an example to get a better understanding of the method
Shortcut to find the square root of a 3 Digit Number
Example 1: √784=?
Step 1: We start by grouping the numbers in pairs of two from the right as follows
7 84
Step 2: To get the ten’s place digit,
We find that nearest square to the first group (7) is 4 and √4=2
Therefore, ten’s place digit=2.
Step 3: To get the unit’s place digit,
We notice that the number ends with 4, So the unit’s place digit of the square root should be either 2 or 8(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(2) and its consecutive number(3) we get,
2 x 3=6
ten’s place digit of original number > Multiplication result
7>6
So we need to select the greater number (8) as the unit’s place digit of the square root.
Unit’s place digit =8
Ans:√784=28
Shortcut to find the square root of any 4 digit number
Example 2: √3721?
Step 1: We start by grouping the numbers in pairs of two from the right as follows
37 21
Step 2: To get the ten’s place digit,
We find that nearest square to the first group (37)is 36 and√36=6
Therefore ten’s place digit=6
Step 3: To get the unit’s place digit,
We notice that the number ends with 1, So the unit’s place digit of the square root should be either 1 or 9(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(6) and its consecutive number(7) we get,
6 x 7=42
ten’s place digit of an original number<Multiplication result
37 < 42
So we need to select the lesser number (1) as the unit’s place digit of the square root.
Unit’s place digit =1
Ans:√3721=61
Example 3: √6889?
Step 1: We start by grouping the numbers in pairs of two from the right as follows
68 89
Step 2: To get the ten’s place digit,
We find that nearest square to the first group (68)is 64 and√64=8
Therefore ten’s place digit=8
Step 3: To get the unit’s place digit,
We notice that the number ends with 9, So the unit’s place digit of the square root should be either 3 or 7(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(8) and its consecutive number(9) we get,
8 x 9 =72
ten’s place digit of an original number<Multiplication result
68 < 72
So we need to select the lesser number (3) as the unit’s place digit of the square root.
Unit’s place digit =3
Ans:√6889=83
Shortcut to find the square root of any 5 digit number
Example 4: √64516
Step 1: We start by grouping the numbers in pairs of two from the right as follows
645 16
Step 2: To get the ten’s place digit,
We find that nearest square to the first group (645)is 625 and√625=25
Therefore ten’s place digit=25
Step 3: To get the unit’s place digit,
We notice that the number ends with 6, So the unit’s place digit of the square root should be either 4 or 6(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(25)and its consecutive number(26)we get,
25 x 26=650
ten’s place digit of an original number<Multiplication result
645< 650
So we need to select the lesser number (4) as the unit’s place digit of the square root.
Unit’s place digit =4
Ans:√64516=254
Shortcut to find the square root of any 6 digit number
Example 5: √126736
Step 1: We start by grouping the numbers in pairs of two from the right as follows. For a 6 digit number, this is how it should be paired.
1267 36
Step 2: To get the ten’s place digit,
We find that nearest square to the first group (1267)is 1225 and√1225=35
Therefore ten’s place digit=35
Step 3: To get the unit’s place digit,
We notice that the number ends with 6, So the unit’s place digit of the square root should be either 4 or 6(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(35)and its consecutive number(36)we get,
35 x 36=1260
ten’s place digit of original number>Multiplication result
1267>1260
So we need to select the greater number (6) as the unit’s place digit of the square root.
Unit’s place digit =6
Ans:√126736=356
Example 6: √207025
Step 1: We start by grouping the numbers in pairs of two from right as follows. For a 6 digit number, this is how it should be paired.
2070 25
Step 2: To get the tenth place digit,
We find that nearest square to the first group (2070) is 2025 and√2025=45. Therefore ten’s place digit=45
Step 3: To get the unit’s place digit,
We notice that the number ends with 5, So the unit’s place digit of the square root should be 5(Refer table).
Skip all the other steps for a number ending in 5
Unit’s place digit =5
Ans:√207025=455
Also, read Square root shortcut Nonperfect squares
Thanks for you giving explanations………..
very nice steps…………………………………
what is the method for sq.root of 625
1. last digit is 5. Unit digit will be 5
2. take 6 from first pair. 4 is near to 6. so sqrt of 4= 2
3. answer is 25.
How to solve 729
The above trick is only for cracking problems in bank exams and work for perfect squares. first have a look at the given answers if there is apart from numbers like none of the above. They you have to check each and every answers..
I found this video to find roots of even 5 digit number in seconds!
https://www.youtube.com/watch?v=IjLuQ1Yt2do
u are always taking the greater no then why there is need to multiply a number with its successor??????
either 3sq or 7sq will give you 9 at unit’s digit.
choose a square close to 7 = sq(2)
2*3 = 6 < 7
therefore digit in unit's place will be the larger number: 9
29*29 = 729
#@!To: Boopathi
√625 = take last 2 digits 25 and remaining is 6. (like this 6 , 25 )
( 1sq=1 , 2sq=4 , 3sq=9 , 4sq=16 , 5sq=25 ,6sq=36 , 7sq=49,
8sq=64 , 9sq=81 , 10sq=100 ).
Now, first see 25= last no. is 5; (where is 5 is coming / 5sq=25.)= take ? 5
Now, again find where 6 is coming. Inbetween 2 sq& 3sq 6 is coming. take always small value.
= and value is 2.
Finally, first value is 5 and second value is 2. =2 5
Answer= 25
————————————–
Question:
You find the √1369 ?
Ans= 37. Follow the above steps.
Thank You. Have a nice day.
Step1:
how to solve 7 digits or more in this shortcut
I dont know about seven digits. But for 6 digits i mentioned above
The complexity increases with number of digits. the more no. of digits..question becomes difficult to solve.
Nothing is impossible in this world. You need right time and right tools.
for 6 digit number, how to find
how to solve 400689
1. Take last number.
2. sq of 9 = 3 so 3 is unit digit
3. Take rest numbers 4006 as single number.
4. Find the number whose square is near to 4006
5. U will find square of 63 is 3969 ~ 4000
7. Ur answer is here dear…633
😉
just take 274576 as a six digit no. the last digit is 6 …which is not a perfect square.then how to find the square root?
Hey you know best coaching center in delhi for bank PO ?? Please tell me..i want to join 1
step 1) In 274576 ,units place is 6
4sq.=16 and 6sq.=36 as 4(less value) & 6(more value) end with 6
the unit place could either 4 or 6
step2) eleminate 76 and takethe rest no.s 2745
find the no. whose square is nearer to 2754
U will find square of 52 is 2704 ~2754
therfore take 52(units place)
step 3) now we should decide weather to take 4(less)or 6(more) as unit digit
take 52 next no. and multiply them 52×53=2756
as 2745<2756, take 4 (less < no.)
therefore the answer is 524
Sir as u said 3 is in unit digit bcoz its square is 9, but last digit of 7,s square is also 9. So how we know it may 3 or 7
step 1.)unit digit is 9
so we should take 3(less value) and 7(more value) as the unit digit
step 2)Take rest numbers 4006 as single number
Find the number whose square is near to 4006
U will find square of 63 is 3969 ~ 4000
Ur answer is here dear…633
step3) 63_ now we should decide either we should take 3 or 7 in the units place
step 4) next no. to 63 is 64, multiply both 63×64=4063<4006
therefore we should take the *less value* as mentioned in step 1)
{take 3(less value) and 7(more value)} i.e, 3 as the digit in units place
Therefore sqaure root of 400689 is 633 (not 6334)
In that case, Multiply the tens digit with consecutive of tens digit. like if tens digit is 6..6 x 7 = 42
now compare 42 with the first 23 digits of the number from left. if the 42 is greater than that number, choose the lesser of the two. If 42 is less than that number, choose greater of the 2 . ATB
633
for √784, as we paired the numbers and got 7 in the first pair, the nearest square to 7 will be 9 right? (3×3) ?? Why is 4 selected?
How do we know which square to take?
Because u always have to take the one less than…and nearest. You cannot take 9..its farther not nearest.
4 is near to 7..as well as less than 7
9 is near but from right side
Observe from left side and you will find wisdom there. >1>2>3>4>5>6>7>8>9
How to solve 4896?
how the nearest square of 7 is 4 can anybody explain……
hello but how to find of a niumber of 7 digits? i.e. 2771291????????????????
how to resolve 961
how to solve53824
How to solve 12996
It’s dere in a lic exam test paper
can this process be used in case of imperfect square?
how to find square root of 6354
How to find the square root / cube root of any number ending with zero? If I follow this method for square root of 2240, then the answer will be 40, but it’s wrong. It is around 47.32. Please suggest a way to find this.