Question

An irrational number is marked on the number line (C) as shown in fig. Then find the value of C.

Answer 1

We know that,

$O{A}^2=A{B}^2+O{B}^2$$\left[1mark\right]$

$=(1{)}^2+(1{)}^2$

$O{A}^2=2$

$\Rightarrow OA=\sqrt{2}$
If we draw an arc with centre O and radius OA, to intersect the numberline at C, then, $OC=\sqrt{2}$

$\Rightarrow$ The value of C is $\sqrt{2}$$\left[1mark\right]$