Question

In the following equation, which variables represent rational numbers and which irrational numbers:

$z^2=0.09$

Answer 1

Step 1: Solving the equation for $z$.

$z^2=0.09$

$z^2-0.09=0$

$z^2-0.3^2=0$

$(z+0.3)(z-0.3)=0$

$z+0.3=0,z-0.3=0$

$z=-0.3,0.3$

Step 2: Identifying whether $-0.3$ and $0.3$ are rational or irrational

We can write $-0.3$ and $0.3$ in $\frac{p}{q}$ form such that $p,q$ are integers and q in non-zero.

$-0.3=\frac{-3}{10}$

$0.3=\frac{3}{10}$

So,$-0.3$ and $0.3$ are rational numbers.

Hence, the varibale represents rational numbers.