Question

निम्न में से कौन सी संख्या पूर्ण वर्ग संख्या नहीं है ?
Which of the following numbers is not a perfect
square number?
64
81
8
144​

Answer 1

Answer:

8 is not a perfect square it is a perfect cube

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which of the following numbers is not a perfect

square number

• 64

• 81

• 8

• 144

TIP :

Step : I Firstly express the given number as a Product of prime factor by using prime factorisation

Step : II Make the pair of similar factors such that the both factors in each pair are equal.

Step : III Take one factor from each pair.

Step : IV . If no factor is left over in grouping (pairs) then the number is perfect square otherwise not

Step : V If no factor left find the product of factor that obtained by taking one factor from each pair. That product is the square root of the given number.

EVALUATION

CHECKING FOR OPTION 1

Here the given number = 64

64 = 2 × 2 × 2 × 2 × 2 × 2

Since no factor is left over in grouping (pairs)

So the number 64 is perfect square

CHECKING FOR OPTION 2

Here the given number = 64

81 = 3 × 3 × 3 × 3

Since no factor is left over in grouping (pairs)

So the number 81 is perfect square

CHECKING FOR OPTION 3

Here the given number = 8

8 = 2 × 2 × 2

Since a prime factor is 2 left over in grouping (pairs)

So the number 8 is not perfect square

CHECKING FOR OPTION 4

Here the given number = 144

144 = 2 × 2 × 2 × 2 × 3 × 3

Since no factor is left over in grouping (pairs)

So the number 144 is perfect square

FINAL ANSWER

Hence the correct option is 8

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