In the following equation, which variables represent rational numbers and which irrational numbers:
$y^{2} = 16$

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Solution

Step 1: Solving the equation for $y$ .
$y^{2} = 16$
$y^{2} - 4^{2} = 0$
$(y + 4) (y - 4) = 0$
$y + 4 = 0, y - 4 = 0$
$y = - 4, 4$
Step 2: Identifying whether $- 4$ and $4$ are rational or irrational
We can write $- 4$ and $4$ in $\frac{p}{q}$ form such that $p, q$ are integers and q in non-zero.
$4 = \frac{4}{1}$
$- 4 = \frac{- 4}{1}$
So, $- 4$ and $4$ are rational numbers.
Hence, the varibale represents rational numbers.

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Similar questions

In the following equations, find which variables x, y, z etc, represent rational or irrational numbers :

(i) $x^{2}$ = 5 (ii) $y^{2}$ = 9

(iii) $z^{2}$ = 0.04 (iv) $u^{2} = \frac{17}{4}$

(v) $v^{2}$ = 3 (vi) $w^{2}$ = 27

(vii) $t^{2} = 0.4$

x, y, z

y^{2} = 16

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

$z^{2} = 0.09$

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

$u^{2} = \frac{15}{4}$

w

w^{2} = 27

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