# In the following equations, find which variables x, y, z etc.

Question:

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) $t^{2}=0.4$

Solution:

(i) Given that $x^{2}=5$

Now we have to find the value of x

Since $x^{2}=5$

$\Rightarrow x=\sqrt{5}$

So it x is an irrational number

(ii) Given that $y^{2}=9$

Now we have to find the value of y

$y^{2}=9$

$\Rightarrow y=\sqrt{9}$

$\Rightarrow y=3$

So y is a rational number

(iii) Given that $z^{2}=0.04$

Now we have to find the value of z

$\Rightarrow z^{2}=\frac{4}{100}$

$\Rightarrow z=\sqrt{\frac{4}{100}}$

$\Rightarrow z=\frac{2}{10}$

$\Rightarrow z=\frac{1}{5}$

So it is rational number

(iv) Given that $u^{2}=\frac{17}{4}$

Now we have to find the value of u

$u^{2}=\frac{17}{4}$

$\Rightarrow u=\sqrt{\frac{17}{4}}$

$\Rightarrow u=\frac{\sqrt{17}}{2}$

So it is an irrational number

(v) Given that $v^{2}=3$

Now we have to find the value of v

$v^{2}=3$

$\Rightarrow v=\sqrt{3}$

So it is an irrational number

(vi) Given that $w^{2}=27$

Now we have to find the value of w

$\Rightarrow w=\sqrt{27}$

$\Rightarrow w=\sqrt{3 \times 3 \times 3}$

$\Rightarrow w=3 \sqrt{3}$

So it is an irrational number

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

Now we have to find the value of t

$\Rightarrow t=\sqrt{0.4}$

$\Rightarrow t=\sqrt{\frac{4}{10}}$

$\Rightarrow t=\frac{2}{\sqrt{10}}$

So it is an irrational number