find out a simple method to find the square of numbers ending with 5s ie 15.25.35.45/....105,115 eic?

Answer 1

EASY!!

Take 15 for example...
Consider the number formed after neglecting the unit place which is 5
For this example its 1
1+1=2
1*2=2
Place this before 25
Wallah! answer is 225

Take 105
Number formed after neglecting 5 is 10
10+1 = 11
10*11=110
Place this before 25
Wallah! answer is 11025

As a general case take a number 10*a+5
where a is the digit in tens place. 0 Numerically: a5
Now place a*(a+1) before 25 and get the answer.

Answer 2

The algebra of this calculation is:
If the given number is n,

We find two numbers such that a = n +e and b= n-e

ab = (n +e) * (n-e) = n^2 - e^2,

n^2 = ab + e^2.



Numbers ending in 5 can be squared mentally very easily.

Leaving the 5, multiply the number left by its next number; insert 25 after the product of this multiplication.

Number is 105
Leaving 5, the number is 10
10 x 11 = 110
Insert 25
11025.

Number is 125
Leaving 5, the number is 12
12 x 13 = 156
Insert 25
15625.

For numbers not ending in 5.

Number is 63

The nearest number ending in zero is 60 which is 3 less than 63.
Add 3 to 63 to get 66.
66x 60 = 3960
Add 3^2 to 3960 to get 3969 which is the square of 63.

Number is 48

The nearest number ending in zero is 50 which is 2 less than 48.
Subtract 2 to get 46.

46 x 50 = 2300
add 2^2 to get 2304 which is the square of 46.

Number 65.
As before the two numbers are
60 and 70.
60 x 70 = 4200 Note that for any number ending in 5 we will get 00 at the last.

Add 5^2 to get 4225.

Answer 3

Let's derive this together.

The number is a...b5
(a...b5)^2 = (10*a....b+5)^2
=100*(a...b)^2+100*a...b+25
=100*a...b(1+a...b)+25
this is the number you get when you multiply two numbers, one is the same original number but with the first digit removed and the other is 1 more than the first. Now, to this product put or attach 25 in the right front.

Thus, the first two digits will be always 25 and the rest is the number obtained by removing the 5 from the first number,multiplied by the number after it.

Example:165^2
16*17=272
so 165^2 =27225

Answer 4

it is easy.
1. suppose you want to find the square of 25.
2. we know that 5*5=25.so the last two digits of square of every number ending in 5 are 25.
3. now take the digit at tens place or before the unit place& add 1 to it
4. as we are finding square of 25 ,2+1=3
5. now multiply 3 with 2 ,i.e. 3*2=6.
6. so the square of 25 is 625

similarly if u wan tto find the square of 105,
10 +1=11
11*10=110
as we know that the last two digits of square of every number ending in 5 are 25.
so the square of 105 = 11025

Answer 5

Consider a number of the form nn5:
This is 10n +5, where n is 1, 2, 3, etc.

Squaring:
(10n + 5)² = 100n² + 100n + 25

Simplifying:
n(n + 1) * 100 + 25

So basically,
1) Find the number before the 5 (e.g. 115 --> 11)
2) Multiply that number times the number after it (11 x 12 = 132).
3) Stick a '25' after it (115² = 13225)

Answer 6

--------Suppose you want to find the square of 25.
--------we know that 5*5=25.so the last two digits of square of every number ending in 5 are 25.
--------now take the digit at tens place or before the unit place& add 1 to it
------now multiply 3 with 2 ,i.e. 3*2=6. the square of 25 is 625
If you want to find the square of 35,
3 +1=4
3*4=12
The last two digits of square of every number ending in 5 are 25.
so the square of 35 = 2025
Doing the same process you find that
square of .........
45 = 2025
55 = 3025
65 = 4225
75 = 5625
85 = 7225
............ and so on

Answer 7

In the number whose square is to be found out,consider the number/s before 5.Let us say this number is 'X'.Add one to it.Multiply the number so obtained by X again.Place the number now obtained before 25 and that is your answer.Let me exemplify this for you.
Let us say you want to find the square of 15.Now the number before five is 1.So here 'X' is 1.Adding 1 to 1 we get 2.Multiplying 2 by 'X' which is 1 in this case we get 2.Now if we place 2 before 25,we get the square of 15 that is 225.
Finding the square of 25,the number before 5 is 2.Adding 1 to 2 we get 3.Multiplying 3 by 2 we get 6.Place 6 before 25 we get 625 which is the square of 25.
Finding the square of 35,the number before 5 is 3.Adding 1 to 3 we get 4.Multiplying 4 by 3 we get 12.Place 12 before 25 we get 1225 which is the square of 35.
To find the square of 55,add 1 to 5 and we get 6.Multiplying 6 by 5 we get 30.Place 30 before 25 and we get the answe 3025
To find the square of 115,the number before 5 is 11.Add 1 to 11 and we get 12.Multiplying 12 by 11 we get 132.By placing 132 before 25 we get the answer 13225