Question

Which of the following statements is valid if $a,b$ are both natural numbers and $a^2=2b^2$?

• A. $a^2$ is even
• B. $a$ is odd
• C. $b^2$ is odd
• D. $b$ can be both even and odd

Answer 1

The correct option is A $a^2$ is even

We know that twice of a natural number is always an even number.
$\therefore a^2$ is even
If square of a number is even, then the number itself must be even
$\Rightarrow a$ is even

Let, $a=2k$, where $k$ is a natural number

$\Rightarrow (2k{)}^2=2b^2$

$\Rightarrow 4k^2=2b^2$

$\Rightarrow b^2=2k^2$

Similarly, $b^2$ and $b$ is also even.