What is the easy way of finding 25^2?

Question

I say first you know all 5's end in 25 when you square them. then you look to see the number begins with 2 so you got 225 then you square 20 to get 400 add them together and you get 625. what do you say.

Answer 1

Your method may work. I tried it on 35^2 which is 1225: 30^2 is 900, then if you take the first 3, in your method you get 325, which when added to 900 is 1225. In order to see if you have a general method, you'll have to do the math. Assume that the number is made of 10n+5, where n is a positive integer >0. Now (10n+5)^2 = 100n^2 + 100n + 25.

Using your method, you would write (10n)^2, then multiply 10n*10 and add 25, to get 100n + 25. The total is then 100n^2 + 100n + 25.

The two expressions are the same, proving that your method works!

Answer 2

25 ² =

(20 + 5) ² =

20 ² + 2(20)(5) + 5 ² =

400 + 200 + 25 =

625

Answer 3

The easiest way of squarring a number ending with 5 is to write 25 at the end. Then look at places before 5 in the number. In 25, it is 2. Number succeeding 2 is 3. Multiply 2 and 3 to get 6. Write 6 in front of 25 to get 625.

Thus,
75^2 = 5625 ( 7x8 = 56)
85^2 = 7225 ( 8x9 = 72)
105^2 = 11025 (10x11 = 110)
995^2 = 990025 (99x100 = 9900)

Hope you have understood the pattern.

Answer 4

I will say:

5^2 = 5 x 5 = [25]
15^2 = 15 x 15 = 2[25]
25^2 = 25 x 25 = 6[25]
35^2 = 35 x 35 = 12[25]
45^2 = 45 x 45 = 20[25]
55^2 = 55 x 55 = 30[25]
... ...

You can see that they are ended in 25.



Then,

5^2 = 5 x 5 = [0]25
15^2 = 15 x 15 = [2]25
25^2 = 25 x 25 = [6]25
35^2 = 35 x 35 = [12]25
45^2 = 45 x 45 = [20]25
55^2 = 55 x 55 = [30]25
... ...

2-0=[2] , 6-2 =[4] , 12-6=[6] , 20-12=[8] , 30-20=[10] ... ...

Answer 5

i say 25 x 20 = 500 and 5 x 25 = 125 so 500 + 125 = 625 ;)

Answer 6

Here's a method my classmate taught me.
I'll try to give you the proof if I can.

.25
*25

This only works when you are squaring a two-digit (I suspect more than two digit though) number with a 5 in the one's place.

Put a 25.

...25

Add 1 to 2.

1 + 2 = 3

Multiply that by 2.

3 * 2 = 6

6 -- 25
625

Your answer is 625

Let's try another one because it's hard to understand on a computer.

.35
*35

Put a 25.

25

3 + 1 = 4
(3)(4) = 12

12 -- 25
1,225

35 * 35 = 1,225

Let's try to prove.

I'll do it only for 2 digit numbers because it'll take a long time for a 3 digit number. I also don't know if it'll work.

.x5
*x5 = (x)(x + 1)(100) + 25

.x5
*x5 = 100x^2 + 100x + 25

(10x + 5)^2 = 100x^2 + 100x + 25

QED
-----
EDIT:

This way may look better.

.....25
....*25
...X25

.....(2+1)5
....*.....25
.........X25

......(3)5
.....*(2)5
.....6..25

The 6 replaces the X. It coud have been two digits that we don't know, but the other one is 0, so I excluded it.

Answer 7

Well squaring a number is just another way of multiplying it by itself. So what 25^2 is saying is what is 25 * 25=? It's really just a simple multiplication problem.

Answer 8

25^2 = 25*25

25*25 = (20*25)+(5*25)

(20*25)+(5*25) = (2*25*10)+(125)

(2*25*10)+(125) = (50*10)+(125)

(50*10)+(125) = (500)+(125)

(500)+(125) = 625

Thats a step by step of how my brain would tackle this problem.

Answer 9

simply multiply 25 times 25
625