In the following equation find the variable and represent it a rational or irrational number: $x^{2} = 5$

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Solution

Given,

$x^{2} = 5$

$\Rightarrow x = \sqrt{5}$

$\sqrt{5}$ is not a perfect square and cannot be expressed in form of a fraction.

Therefore, given number is irrational.

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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

x^{2} = 7

t

t^{4} = 256

w

w^{2} = 27

x, y, z

z^{2} = 0.02

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