Locate √5 on the number line.

Step 1:

Draw a number line. Mark points O and A such that O represents the number zero and

A represents the number 2. i.e., OA = 2 unit

Step 2:

Draw AB ⊥ OA such that AB = 1unit.

Step 3:

Join OB

In right triangle OAB, by Pythagorean theorem,

OB² = OA² + AB²

OB² = 2² + 1²

OB² = 4 + 1

OB = √5

Step 4:

With O as centre and radius OB, draw an arc to intersect the number line at C on the right side of O. Clearly OC = OB = √5 . Thus, C corresponds to √5 on the number line.