# Shortcut Squaring Techniques

Friends, we have already discussed two shortcut methods for finding squares of a given number. You can find the Shortcut method 1 from here and Shortcut method 2 from here. Today we are giving you another simple method to find the squares of numbers ending with 9 and 1. This method is shared by our friend Mr. Hareesh Kumar. As you know, both the numbers 9 and 1 have a sort of similarity and make us easy to find the squares of such numbers within fraction of seconds. Let us have a look at them, lets start with numbers ending with “9”:

NUMBERS ENDING WITH 9:
Let me start from smaller numbers.
Sol: We know that, 10^2 = 100
Step – 1: Consider the 10’s digit of “10”, which is 1.
Step – 2: Double the number in the ten’s digit (i.e., 1*2 = 2)
(We know that, the unit’s digit of the square of a number ending with 9 will be 1)
Step – 3:  Subtract the doubled number from the number formed by eliminating a zero (0)
from the resultant of the 10^2. (i.e., 10 – 2 = 8)
Step – 4: This is the final step, place 8 before 1, hence the answer becomes “81”
Ex. 2: 29^2 = ?
Sol: 30^2 = 900; 3*2 = 6 --> 90 – 6 = 84
Therefore, 29^2 = 841
Ex. 3: 139^2 =?
Sol: 140^2 = 19600 ; 14*2 = 28 --> 1960 – 28 = 1932
Therefore, 139^2 = 19321
Ex. 4: 89^2 =?
Sol: 90^2 = 8100; 9*2 = 18 --> 810 – 18 = 792
Therefore, 89 * 89 = 7921
Ex. 5: 249^2 =?
Sol: 250^2 = 62500; 25*2 = 50 --> 6250 – 50 = 6200
Therefore, 249^2 = 62001

NUMBERS ENDING WITH 1:
Ex. 6: 11^2 =?
Sol: We know that, 10^2 = 100
Step 1: Double the tens’ digit of 10. (i.e., 1*2 = 2)
Step 2: By eliminating zero in the unit’s place in the resultant of 10^2, we get 10.
Add 2 to this 10 --> 12
Step 3: We know that the result obtained by squaring a number ending with 1 will also contain 1 in its unit’s digit.
Step 4: Place the 12 before 1 --> Answer = 121
Ex. 7: 121^2 =?
Sol: 120^2 = 14400; 12*2 = 24 --> 1440+24 = 1464
Therefore, 121^2 = 14641
Ex. 8: 91^2 =?
Sol: 90^2 = 8100; 9*2 = 18 --> 810+18 = 828
Hence, 91^2 = 8281
Ex.9: 231^2 =?
Sol: 230^2 = 52900; 23*2 = 46 --> 5290+46 = 5336
Hence, 231^2 = 53361
Ex. 10: 501^2 =?
Sol: 500^2 = 250000; 50*2 = 100 --> 25000+100 = 25100
Hence, 501^2 = 251001

Thanks to Hareesh Kumar for the update :)

Already know this method ? You can find more shortcuts from here

1. Good one bro. Thank you

2. calculate the square of 45

let take 45= 4+5 that is a=4 b=5 it means (a+b)^2 that is (4+5)^2
(a+b)^2 = a^2 + 2 * a * b + b^2
(4+5)^2=4^2 +2 *4*5 +5^2

4^2=16
2 *4*5=40
5^2= 25
2 5
4 0
1 6
----------------------------------------------
2 0 2 5

1. Bro, why do you elaborate this much.... You have a simple method that completes in a step for numbers ending with "5".... Example: 45^2 = (4*5) | 25 = 2025

In general, Square of X5 will be equal to: X*(X+1) | 25

2. oh! super friend!

3. thank u so much very quick method...plz share more tricks.

3. calculate the square of 45

let take 45= 4+5 that is a=4 b=5 it means (a+b)^2 that is (4+5)^2
(a+b)^2 = a^2 + 2 * a * b + b^2
(4+5)^2=4^2 +2 *4*5 +5^2