Question

If $a^2$ends in $9,$then $a^3$ ends in $7.$

State whether the statement is true (T) or false (F).

• A. True
• B. False

Answer 1

The correct option is B False

Verify the given statement

Given that if $a^2$ends in $9,$then $a^3$ end in $7$

Case 1: Let $a$ be $13$

$\therefore a^2={\left(13\right)}^2=169$

$a^3={\left(13\right)}^3=2197$

Here, $a^2$ends in$9$ and$a^3$ end in $7$

Case 2: Let $a$ be $17$

$\therefore a^2={\left(17\right)}^2=289$

$a^3={\left(17\right)}^3=4913$

Here, $a^2$ends in$9$ and$a^3$ do not end in $7$

Considering the above two cases we can say that the given statement is not always true

Hence, the given statement is false