In the following equation, find which variables $x, y, z$ etc. represent rational or irrational numbers:$ z^{2}=0.04 $
Given:
\( z^{2}=0.04 \)
To do:
We have to find whether $z$ represents a rational number or an irrational number.
Solution:
A rational number can be expressed in either terminating decimal or non-terminating recurring decimals and an irrational number is expressed in non-terminating non-recurring decimals.
$z^2=0.04$
$\Rightarrow z^2=(\pm \sqrt{0.2})^2$
$\Rightarrow z=\pm 0.2$
$0.2$ is a rational number.
Therefore, \( z \) is a rational number.
Related Articles
- In the following equation, find which variables $x, y, z$ etc. represent rational or irrational numbers:\( y^{2}=9 \)
- In the following equation, find which variables $x, y, z$ etc. represent rational or irrational numbers:\( x^{2}=5 \)
- In the following equation, find which variables $x, y, z$ etc. represent rational or irrational numbers:\( v^{2}=3 \)
- In the following equation, find which variables $x, y, z$ etc. represent rational or irrational numbers:\( w^{2}=27 \)
- In the following equation, find which variables $x, y, z$ etc. represent rational or irrational numbers:\( t^{2}=0.4 \)
- In the following equation, find which variables $x, y, z$ etc. represent rational or irrational numbers:\( u^{2}=\frac{17}{4} \)
- Subtract $3 x y+5 y z-7 z x$ from $5 x y-2 y z-2 z x+10 x y z$.
- Find the following products:\( \frac{-4}{27} x y z\left[\frac{9}{2} x^{2} y z-\frac{3}{4} x y z^{2}\right] \)
- Verify that \( x^{3}+y^{3}+z^{3}-3 x y z=\frac{1}{2}(x+y+z)\left[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}\right] \)
- Find the following products:\( \frac{-8}{27} x y z\left(\frac{3}{2} x y z^{2}-\frac{9}{4} x y^{2} z^{3}\right) \)
- Factorise:(i) \( 4 x^{2}+9 y^{2}+16 z^{2}+12 x y-24 y z-16 x z \)(ii) \( 2 x^{2}+y^{2}+8 z^{2}-2 \sqrt{2} x y+4 \sqrt{2} y z-8 x z \)
- Simplify each of the following expressions:\( (x+y-2 z)^{2}-x^{2}-y^{2}-3 z^{2}+4 x y \)
- Factorise:\( 4 x^{2}+9 y^{2}+16 z^{2}+12 x y-24 y z-16 x z \)
- Write the following in the expanded form:\( (\frac{x}{y}+\frac{y}{z}+\frac{z}{x})^{2} \)
- If $x=1,\ y=2$ and $z=5$, find the value of $x^{2}+y^{2}+z^{2}$.
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies