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Which one cannot be the square of a natural number ?
- a)2116
- b)2304
- c)2202
- d)2209
Correct answer is option 'C'. Can you explain this answer?
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Which one cannot be the square of a natural number ?a)2116b)2304c)2202...
Square number can never end in 2,7
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Which one cannot be the square of a natural number ?a)2116b)2304c)2202...
Solution:
To check whether a number is a perfect square or not, we can use the prime factorization method. We factorize the given number into its prime factors and check if each prime factor has an even power. If yes, then the number is a perfect square, otherwise not.
Let's factorize the given options:
a) 2116 = 2^2 x 23^2
b) 2304 = 2^7 x 3^2
c) 2202 = 2 x 3 x 367
d) 2209 = 47^2
Now, we can see that options a), b), and d) have all prime factors with even powers, so they are perfect squares. However, option c) has a prime factor 367 with an odd power 1, so it cannot be a perfect square.
Therefore, the correct answer is option C) 2202.
To check whether a number is a perfect square or not, we can use the prime factorization method. We factorize the given number into its prime factors and check if each prime factor has an even power. If yes, then the number is a perfect square, otherwise not.
Let's factorize the given options:
a) 2116 = 2^2 x 23^2
b) 2304 = 2^7 x 3^2
c) 2202 = 2 x 3 x 367
d) 2209 = 47^2
Now, we can see that options a), b), and d) have all prime factors with even powers, so they are perfect squares. However, option c) has a prime factor 367 with an odd power 1, so it cannot be a perfect square.
Therefore, the correct answer is option C) 2202.
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