Question

Write true $\left(T\right)$ or false $\left(F\right)$ for the following statements:
If $a^2$ ends in an even number of zeros, then $a^3$ ends in an odd number of zeros.

Answer 1

Step: State true or false

Given statement: If $a^2$ ends in an even number of zeros, then $a^3$ ends in an odd number of zeros.

Consider $a=100$
$\Rightarrow a^2=(100{)}^2=100\times 100=10000,$
which ends in even number of zeros

Now, $a^3=(100{)}^3=100\times 100\times 100=1000000,$
which also ends in even number of zeros

Therefore, if $a^2$ ends in an even number of zeros, then $a^3$ does not always ends in an odd number of zeros.

Hence, the given statement is false.