Question

Represent √2,√3,√5 on real line

Answer 1

QUESTION:

Represent each of the following numbers √2,√3 and √5 on real line.

SOLUTION:

Let X'OX be a horizontal line , taken as the x-axis and let O be the origin. Let O represent 0.

Take OA = 1 unit and draw ⊥ OA such that AB = 1 unit.

Join OB . Then ,

$\sf \: OB = \sqrt{OA^{2} + AB^{2} } \\ \\ \sf \: \sqrt{ {1}^{2} + {1}^{2} } \\ \\ \sf \: = \sqrt{2} units.$

With O as centre and OB as radius, draw on arc , meeting OX at P.

Then, OP = OB = √2 units.

thus , the point P represents √2 on the real line.

Now , draw BC ⊥ OB such that BC = 1 unit.

Join OC. then ,

$\sf \: OC = \sqrt{ {OB}^{2} +CB^{2} } \\ \: \\ \sf \: \sqrt{( \sqrt{2)^{2} } + {1}^{2} } \\ \\ \sf \: = \sqrt{3} units$

With O as centre and OC as radius , draw an arc, meeting OX at Q , then,

OQ = OC = √3 units.

thus , the point Q represents √3 on the real line.

Now, draw CD ⊥OC such that CD = 1 unit.

Join OD. Then ,

$\sf \: OD = \sqrt{ {OC}^{2} + CD^{2} } \\ \\ \sf \: \sqrt{(\sqrt{3)^{2} }+ {1}^{2} } \\ \\ \sf \: = \: \sqrt{5 \: units.}$

With O as centre and OE as radius draw an arc , meeting OX at R. Then , OR =OE= √5 units.

Thus , the point R represents √5 on real line.