1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Show how $\surd 5$can be represented on the number line.

Open in App
Solution

## To represent $\surd 5$ on number line let us follow the given procedure:Step 1: Let us assume line $AB$ be of $2$unit on a number line.Step 2: At $B$, draw a perpendicular line $BC$ of length $1$ unit.Step 3: Join $CA$Step 4: Now, we get $ABC$ as a right-angled triangle.On applying Pythagoras theorem,$A{B}^{2}+B{C}^{2}=C{A}^{2}={2}^{2}+{1}^{2}\phantom{\rule{0ex}{0ex}}⇒C{A}^{2}=5\phantom{\rule{0ex}{0ex}}⇒CA=\surd 5.$Thus, $CA$ is a line of length $\surd 5$ unit.Step 5: Considering $CA$ as a radius and $A$ as a centre draw an arc touching the number line.The point at which number line get intersected by arc is at $\surd 5$ distance from $0$ because it is a radius of the circle whose centre was $A$.Hence, $\surd 5$ is represented on the number line as shown in the figure.

Suggest Corrections
840
Join BYJU'S Learning Program
Related Videos
The Number Line
MATHEMATICS
Watch in App
Join BYJU'S Learning Program