Question

Locate $\sqrt{17}$ on the number line.

Answer 1

Locate the given number on a number line

Given irrational number, $\sqrt{17}$

$17$ can be written as the sum of square of two natural number as:

$$\begin{gathered} 17=4^2+1^2 \\ \Rightarrow \sqrt{17}=\sqrt{4^2+1^2} \end{gathered}$$

Therefore on number line

Consider $OA=4\mathrm{units}$

Draw a perpendicular to $OA$ that is $AB$ of $1\mathrm{unit}$.

Now join $OB$.

On applying Pythagoras theorem,

We obtain $OB=\sqrt{17}$

Draw an arc with center $O$ and radius $OB$ using compass such that its intersects the number line on the point $C$.

Then, we get, point $C$ corresponding to $\sqrt{17}$, or we can say $OC=\sqrt{17}$ units.

Hence, we obtain $\sqrt{17}$ on the number line.