Question

For an integer $a$, $a^3$ is always greater than $a^2$. 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, $a^3$ is always greater than $a^2$

Let us assume $a=3$.

$\therefore a^3={\left(3\right)}^3=27$ and

$a^2={\left(3\right)}^2=9$

$$\begin{gathered} 27>9 \\ \Rightarrow a^3>a^2 \end{gathered}$$ ….$\left[1\right]$

Let us assume $a=1$.

$\therefore a^3={\left(1\right)}^3=1$ and

$a^2={\left(1\right)}^2=1$

$$\begin{gathered} 1=1 \\ \Rightarrow a^3=a^2 \end{gathered}$$ …$\left[2\right]$

Let us assume $a=-2$.

$\therefore a^3={\left(-2\right)}^3=-8$ and

$a^2={\left(-2\right)}^2=4$

$-8<4$

$\Rightarrow a^3<a^2$ …$\left[3\right]$

From $\left[1\right]$, $\left[2\right]$ and $\left[3\right]$ we can say that $a^3$ is not always greater than $a^2$

Hence, the given statement is False.