HOW TO FIND UNIT DIGIT OF SQUARE

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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