Question

Which one of the following can’t be a square of a natural number?
A. 30976
B. 75625
C. 28561
D. 143642

Answer 1

Hint: To check if the number is a square of a natural number, we will take out the square root of the given number, if the square root obtained is a whole number, then we say that the given number is a square of natural number.

Complete Step-by-Step solution:
We proceed according to the above explained method.
Now we are given options in the question. We will take them separately and check if we obtain a natural number by taking the square root of them.
Now taking out the square root of the given numbers:
(a)\[\sqrt{30976}=176\], we obtained a natural number.
Therefore, 30976 is a square of a natural number.
(b) \[\sqrt{75625}=275\] again, we obtained a natural number.
 Therefore, 75625 is a square of a natural number.
(c) \[\sqrt{28561}=169\] again, we obtained a natural number.
Therefore, 28561 is a square of a natural number.
(d)\[\sqrt{143642}=379.001\], which is a number in fraction or in decimal point, not a natural number.
Therefore, 143642 isn’t a square of a natural number.

Hence, we get our result as 143642 isn’t a square of a natural number, which is option (d).

Note: When square root is applied to a number, we get both positive and negative parts of the square root. The possibility of error in this question can be taking the negative part of the question which is wrong because natural numbers only contain positive integers and not negative.