Question

An irrational number, D is marked on the number line as shown in the figure. The value of CD is ________.

Answer 1

By Pythagoras theorem we know that,

$A{C}^2=A{B}^2+C{B}^2$

$A{C}^2=(4{)}^2+(1{)}^2$

$A{C}^2=16+1$

⇒ $AC=\sqrt{17}$

Now we can see that with AC as radius, an arc is being formed which intersects the number line at D.

Therefore, AC = CD = Radius of the arc = $\sqrt{17}$ units.

∴ The value of $CD$ is $\sqrt{17}$ units.