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Real Numbers

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Question

Let $a$ and $b$ be co-prime, thus $a^{2}$ and $b^{2}$ are

A

co-prime

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B

not co-prime

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C

odd numbers

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D

even numbers

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Solution

The correct option is A co-prime
If the H.C.F of two numbers are $1$ they are said to be co-prime.
Now it is given $a, b$ are co-prime numbers.
so, H.C.F. of $a, b = 1$
Therefore, H.C.F of $a^{2}$ & $b^{2} = 1$ as the factor of $a^{2}$ and $b^{2}$ will be $1, a, a^{2}$ and $1, b, b^{2}$ respectively.

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