Which of the following numbers are the squares of even numbers ?
(a) 441
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Answer:
44 is the square of even numbers
Answer:
Which of the following numbers are squares of even numbers?
121,225,256,324,1296,6561,5476,4489,373758
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Correct option is
A
256,324,1296,5476
The numbers whose last digit is odd can never be the square of even numbers.
So, we have to leaves out 121,225,6561 and 4489 leaving only 256,324,1296,5476 and 373758
For each number, use prime factorization method and make pairs of equal factors.
(i) 256=2×2×2×2×2×2×2×2
=(2×2)×(2×2)×(2×2)×(2×2)
There are no factors that are not paired.
Hence, 256 is a perfect square.
The square of an even number is always even.
Hence, 256 is a perfect even square.
(ii) 324=2×2×3×3×3×3
=(2×2)×(3×3)×(3×3)
There are no factors that are not paired.
Hence, 324 is a perfect square.
The square of an even number is always even.
Hence, 324 is a perfect even square.
(iii) 1296=2×2×2×2×3×3×3×3
=(2×2)×(2×2)×(3×3)×(3×3)
There are no factors that are not paired.
Hence, 1296 is a perfect square.
The square of an even number is always even.
Hence, 1296 is a perfect even square.
(iv) 5476=2×2×37×37
=(2×2)×(37×37)
There are no factors that are not paired.
Hence, 5476 is a perfect square.
The square of an even number is always even.
Hence, 5476 is a perfect even square.
(v) 373758=2×3×7×11×809
Here, each factor appears only once, so grouping them into pairs of equal factors is not possible.
It means that 373758 is not the square of an even number.
Hence, the numbers that are the squares of even numbers are 256,324,1296 and 5476.