Find Square Of a number with Simple and faster Ways

Find Square of a number ending with 5:

1.1 Example: Let’s find out square of 25.

Break the number to two parts with 2 as first part and 5 as second part
Find multiplication of 2 and (2+1), i.e 2 x 3 = 6
Find square of 5, i.e. 25
Hence, our answer, 252 = 6 25=625

1.2 Lets take another example, i.e. 65

65 = 6 5
6 x (6+1) = 42
Square of 5 = 25
Hence, 652 = 42 25 = 4225

1.3.Let’s take a 3 digit number, i.e. 125

125 = 12 5
12 x (12 + 1) = 156
Square of 5 = 25
Hence, 1252 = 156 25 = 15625
This way this rule can be used to calculate square of numbers ending with 5 without help of pen and paper.


Find Square of a number which is adjacent to a number that ends with 0 or 5:
We can easily find out square of a number that ends with 0 or 5, e.g. 10, 15, 20, 25, 30 etc.Now we will see how to find out square of an adjacent number like 11, 9, 16, 14, 21, 19 etc

2.1 Example: Let’s find out square of 31.

We know square of 30, i.e. 302 = 900
Now, 312 = 302 + (30 + 31) = 900 + 61 = 961

2.2 Lets find out square of 46

a. 452 = 2025
b. 462 = 452 + (45 + 46) = 2025 + 91 = 2116

2.3 Lets find out square of 71

702 =4900
712 = 702 + (70 + 71) = 4900 + 141 = 5041
Now, let’s find out numbers which are 1 less to numbers ending with 5 or 0

2.4 Find square of 14

a. 152 = 225
b. 142 = 152 – (14 + 15) =225 – 29 = 196

2.5 Find square of 29

a. 302 = 900
b. 292 = 302 – (29 + 30) = 900 – 59 = 841


Find out Square of a number near 100:
Let’s find out square numbers which are close to 100 and are lesser than 100.

3.1 Find square of 97

a. 97 is 3 less than 100 (i.e. -3)
b. 972 = 97 -3 / 032 = 94 / 09 = 9409 (There should be two digits (09 instead of 9) after ‘/’)

3.2 Find square of 96

a. 96 is 4 less than 100 (i.e. -4)
b. 962 = 96 -4 / 042 = 92 / 16 = 9216

3.2 Find square of 87

a. 87 is 13 less than 100 (i.e. -13)
b. 872 = 87 -13 / 132 = 74 / 169 =7569 (There should be two digits(69 out of 169), hence 1 is carry forwarded from 169 and added to 4 of 74)

Let’s find out square of numbers which are close to 100 and are greater than 100.

1.Find square of 103

103 is 3 greater than 100 (i.e. +3)
1032 = 103 +3 / 032 = 106/09 = 10609

2.Find square of 107

107 is 7 greater than 100 (i.e. +7)
1072 = 107 +7 / 072 = 114 / 49 = 11449

3.Find square of 113
113 is 13 greater than 100 (i.e. +13)
1132 = 113 +13 / 132 = 126 / 169 = 12769 (1 is carry forwarded from 169)


I hope this material was helpful to you.


Answer of Previous Puzzles:

PZ1:

• The state of the door depends on the number of times it will be visited as follows:if the number of times it is visited is even - the door will end up closedotherwise - the door will end up open .
• The number of times each door is visited is directly related to the number of dividers the number (door number) has (including 1 and itself).
• For example, every prime number door will be visited twice, and hence ends up closed
• So,the perfect square doors only open(including with 1)

Answer: only 1,4,9,16,25,36,49,64,81,100 will be open.

PZ2:
way1:100 th person entering will have #1 or #100 to sit..consider,crazy man(whose actual ticket no is 1) sits in #31.persons 2 to 30 occupy correct seats.now 31st person sits suppose in #32 and 32nd person may sit in #1 or even he can go for any random inbetween #33,#100..(if he chooses #1 then all others will havecorrect seats) and if he chooses any no in betwen 33,100 the successors can repeat the process and finally only either seat #1 or #100 will be empty.

so the probability is 0.5

way2:
Following this sequence, we get the following recursive relationship:
P(n) = P(n-1)(1/(101-n))
If we start to work this relationship out, we get a surprising answer:
P(1) = 1/100
P(2) = 1/99
P(3) = 1/98
and, more generally,
P(n) = 1/(101-n) ( for n<100)

so the probability is 1/2