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^{2}? How about 25

^{2}? How would you find the answer? Can you tell the answer in 3 to 5 seconds?

Yes, there is a fast way of squaring numbers ending in 5. The method lies on the pattern being formed by the numbers upon squaring as related to the numbers being squared. Let's observe the pattern of the numbers.

5

^{2}= 25

15

^{2}= 225

25

^{2}= 625

35

^{2}= 1,225

We know already that 5

^{2}is equal to 25, that is 5

^{2}= (5)(5) = 25. Since the remaining numbers end in 5, expectedly the results should also end in 25.

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**1**5

^{2}=

**2**25

**5**

__2__^{2}=

**6**25

**5**

__3__^{2}=

**12**25

Now, let us look for the relationship between the remaining digits (aside from 5 and 25). The numbers are

**1**and

**2**where 2 = (

**)(2)**

__1__**2**and

**6**6 = (

**)(3)**

__2__**3**and

**12**12 = (

**)(4)**

__3__In the first pair of numbers, 2 is the product of 1 and the next consecutive number which is 2. Same as with the second pair, 6 is the result when 2 is multiplied to the number next to it which is 3. In the third pair, 12 is the product of 3 and 4.

Hence, when you square a number ending in 5, you simply multiply the remaining digit of the number, aside from 5, to the number next to it. Let us try to use it in the following numbers.

- What is 45
^{2}?

*solution:*

Since the other digit aside from 5 is 4, multiply it to the number next to it which is 5. That is

(4)(5)= 20

Affix 25 to the result. The result is 2025.

Hence,

**45**^{2 }=. 2,025- Find the exact value of 55
^{2}?

*solution:*

(5)(6) = 30

Affix 25 to it. That is 3,025.

Hence,

**55**.

^{2}= 3025Now, it's your turn. Try to find the value of the following in 5 seconds.

- 65
^{2}

- 75
^{2}

- 85
^{2}

- 95
^{2}

- 105
^{2}

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