Question

Show $-$$\sqrt{2}$, $\sqrt{5}$ on the number line.

Answer 1

Let X'OX be a horizontal line taken as the x-axis and O be the origin representing 0.
Take OA = 1 unit and AB ⊥ OA, such that AB = 1 unit.
Join OB.
Now,
OB = $\sqrt{O{A}^2+A{B}^2}=\sqrt{1^2+1^2}=\sqrt{2}$ units
Taking O as the centre and OB as the radius, draw an arc, meeting OX' at Q.
We have:
OQ = OB = $\sqrt{2}$ units
Thus, point Q represents $-\sqrt{2}$ on the number line.
Now, draw CD ⊥ OD, such that OD = 2 units and CD = 1 unit.
Join OC.
We have:
OC = $\sqrt{O{D}^2+C{D}^2}=\sqrt{{\left(2\right)}^2+1^2}=\sqrt{5}$ units
Taking O as the centre and OD as the radius, draw an arc, meeting OX' at P.
We have:
OC = OP = $\sqrt{5}$units
Thus, point Q represents $-\sqrt{5}$ on the number line.