Squaring any two digit number ending in five

Squaring any two digit number ending in five is very easy and straightforward. We will show you how to do this in this lesson with a very good mnemonic. First, look at the following multiplication.

Squaring-numbers-ending-in-five-image
Did you make the following important observation? The answer always ends in 25.

This will be the case when you square any two digit number ending with 5.

Now, how did we get the number(s) before 25? There numbers before the 25 are 6, 20, and 2. It is not difficult to see at all!

Look for the number in the tens place. For the multiplications above, these are 2, 4, and 1.

Multiply each number by its next higher digit. The next higher digit for 2 is 3 and the next higher digit for 8 is 9.

So,

2 × 3 = 6

4 × 5 = 20

1 × 2 = 2

Put these numbers on the left of 25.

Other examples showing how squaring any two digit number ending in five is easy and straightforward.

Example #1: 35 × 35

The digit in the tens place is 3.

Multiply 3 by its next higher digit, which is 4.

3 × 4 = 12

Write down 12 and put 25 next to it.

The answer is 1225.

Example #2: 55 × 55

The digit in the tens place is 5.

Multiply 5 by its next higher digit, which is 6.

5 × 6 = 30

Write down 30 and put 25 next to it.

The answer is 3025.

Example #3: 95 × 95

The digit in the tens place is 9.

Multiply 9 by its next higher digit, which is 10.

9 × 10 = 90

Write down 90 and put 25 next to it.

The answer is 9025.

Example #4: 195 × 195

This time, you are looking not just for the digit in the tens place, but for the digits in the tens and hundreds place. The digit in the tens and hundreds place is 19.

Multiply 19 by its next higher number, which is 20.

19 × 20 = 380

Write down 380 and put 25 next to it.

The answer is 38025.

Important note:

Before you can really apply these tricks, you must know your multiplication table by heart.

Have you learned your multiplication table yet?

If having problems to learn the multiplication table by heart, have you tried finger multiplication ?

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