# HOW TO FIND UNIT DIGIT OF SQUARE

The unit digit of a perfect square can be only

0, 1, 4, 5, 6 or 9

The square of a number having :

1 or 9 at the units place ends in 1

2 or 8 at the units place ends in 4

3 or 7 at the units place ends in 9

4 or 6 at the units place ends in 6

5 at the units place ends in 5

To find the unit digit of square of a number, we don't have to evaluate square of the given number. We can find the unit digit of square of a number by using the unit digit in the base of the given square.

Alternative Method :

Consider the square of 64.

642 = 64 x 64

To find the unit digit of 642, multiply the 4's alone in the two 64's on the right side.

4 x 4 = 16

In 16, the unit digit is '6'.

Therefore, the unit digit of 642 is '6'.

Find the unit digit of the following squares :

Example 1 :

142

Solution :

In 142, the base is '14'.

Since the unit digit of the base 14 is '4', the resulting number of 142 will end in '6'.

So, the unit digit of 142 is '6'.

Justification :

142 = 14 x 14 = 196

In 196, the unit digit is '6'.

Example 2 :

782

Solution :

In 782, the base is '78'.

Since the unit digit of the base 78 is '8', the resulting number of 782 will end in '4'.

So, the unit digit of 782 is '4'.

Alternative Method :

782 = 78 x 78

Multiply only the unit digits on the right side.

8 x 8 = 64

The unit digit of 64 is '4'.

Therefore, the unit digit of 782 is '4'.

Example 3 :

272

Solution :

In 272, the base is '27'.

Since the unit digit of the base 27 is '7', the resulting number of 272 will end in '9'.

So, the unit digit of 272 is '9'.

Alternative Method :

272 = 27 x 27

Multiply only the unit digits on the right side.

7 x 7 = 49

The unit digit of 49 is '9'.

Therefore, the unit digit of 272 is '9'.

Example 4 :

412

Solution :

In 412, the base is '41'.

Since the unit digit of the base 41 is '1', the resulting number of 412 will end in '1'.

So, the unit digit of 412 is '1'.

Alternative Method :

412 = 41 x 41

Multiply only the unit digits on the right side.

1 x 1 = 1

The unit digit of 1 is '1'.

Therefore, the unit digit of 412 is '1'.

Example 5 :

2352

Solution :

In 2352, the base is '235'.

Since the unit digit of the base 235 is '5', the resulting number of 2352 will end in '5'.

So, the unit digit of 2352 is '5'.

Alternative Method :

2352 = 235 x 235

Multiply only the unit digits on the right side.

5 x 5 = 25

The unit digit of 25 is '5'.

Therefore, the unit digit of 252 is '5'.

Example 6 :

14362

Solution :

In 14362, the base is '1436'.

Since the unit digit of the base 1436 is '6', the resulting number of 14362 will end in '6'.

So, the unit digit of 14362 is '6'.

Alternative Method :

14362 = 1436 x 1436

Multiply only the unit digits on the right side.

6 x 6 = 36

The unit digit of 36 is '6'.

Therefore, the unit digit of 14362 is '6'.

Example 7 :

3170522

Solution :

In 3170522, the base is '317052'.

Since the unit digit of the base 317052 is '2', the resulting number of 3170522 will end in '2'.

So, the unit digit of 3170522 is '4'.

Alternative Method :

3170522 = 317052 x 317052

Multiply only the unit digits on the right side.

2 x 2 = 4

The unit digit of 4 is '4'.

Therefore, the unit digit of 3170522 is '4'.

Example 8 :

1002

Solution :

In 1002, the base is '100'.

Since the unit digit of the base 100 is '0', the resulting number of 1002 will end in '0'.

So, the unit digit of 1002 is '0'.

Alternative Method :

1002 = 100 x 100 = 10000

The unit digit of 10000 is '0'.

Therefore, the unit digit of 1002 is '0'.

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