Question

Represent the number `sqrt(7)` on the number line.

Answer 1

Let us find `sqrt(5)`.
Draw a number line.
Mark a point O representing zero.
Take point A on number line such that OA = 2
Construct AB ⊥ OA such that AB = 1 unit.
∴ ΔOAB is a right triangle.
In ΔOAB, (OB)² = (OA)² + (AB)²  (Pythagoras' Theorem)
∴ (OB)² = 2² + 1²
∴ (OB)² = 5
⇒ OB = `sqrt(5)`

Now, let us find `sqrt(6)`.
Construct BC ⊥ OB, such that BC = 1 unit.
∴ ΔOBC is a right triangle.
In ΔOBC, OC² = OB² + BC²  (Pythagoras' Theorem)
∴ OC² = `(sqrt(5))^2 + 1^2`
∴ OC² = 6
⇒ OC = `sqrt(6)`

Now, let us find `sqrt(7)`.
Construct CD ⊥ OC, such that CD = 1 unit.
In ΔOCD, OD² = OC² + CD²  (Pythagoras' Theorem)
∴ OD² = `(sqrt(6))^2 + 1^2`
∴ OD² = 7
⇒  `sqrt(7)`
Draw an arc of radius OD and centre O and let it intersect the number line at point E.
∴ `sqrt(7)` is thus marked at point E on the number line.