Question

Following number cannot be perfect square.give reason.
a. 3727
b. 8178​

Answer 1

Given : a. 3727

b. 8178​

To Find :  given numbers can be perfect square or not

Solution:

10²  =100

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9²  81

Square of any number ends with 00 , 1 , 4  , 5 , 6  or 9 only

3727  and 8178 does not have unit digit as  0 , 1 , 4  , 5 , 6  or 9

Hence given numbers can not be a perfect square

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Answer 2

Given:

a. 3727

b. 8178

To find:

The given numbers are not perfect squares. Give reason.

Solution:

a. 3727   b. 8178

• Observe the unit digits of the given numbers. 7 is the unit digit of 3727. 8 is the unit digit of 8178.

• The perfect Square number always ends with 0, 1, 4, 5, 6, and 9.

• The number of zeros at the end of a square number is always even.

• A number ending with an odd number of zeros is never a perfect square.

• Square numbers never end with 2, 3, 7, or 8. Hence, the given numbers 3727 and 8178 are not a perfect square numbers

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By just observing the digits at one's place, tell which of the following can be perfect squares? 1026,1022,1024,1027

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