Question

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

• A. $\sqrt{7}$
• B. $\sqrt{5}$
• C. $\sqrt{3}$
• D. $\sqrt{2}$

Answer 1

The correct option is D

$\sqrt{2}$

We know that,

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

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

$O{A}^2=2$

$\Rightarrow OA=\sqrt{2}$
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 $\sqrt{2}$