# How to locate √x on number ...

How to locate √x on number line

Sia 🤖 7 months, 2 weeks ago

We can write 10 as
{tex}10 = 9 + 1 = 3^2 + 1^2{/tex}
Draw OA = 3 units, on the number line
Draw BA = 1 unit, perpendicular to OA.
Join OB
Figure: Now, by Pythagoras theorem,
{tex}OB^2 = AB^2 + OA^2\\ OB^2 = 1^2 + 3^2 = 10{/tex}
Taking O as centre and OB as a radius, draw an arc which intersects the number line at point C.
Clearly, OC corresponds to {tex}\sqrt{10}{/tex} on the number line.

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