Question

represent √6 on number line​

Answer 1

Step-by-step explanation:

Let OA = 2 units and let AB perpendicular to a OA such that AB = 1 unit.

Join OB. Then, OB = √(OA^2 + AB^2) = √(2^2 + 1^2) = √5. [By Pythagoras theorem]

With O as centre and OB as radius, draw an arc, meeting at P on the number line.

Then, OP = OB = √5.

Thus, P represents √5 on the real line.

Now, draw BC perpendicular to OB and set off BC = 1 unit.

Join OC. Then, OC = √(OB^2 + BC^2) = √(√5^2 + 1^2) = √6. [By Pythagoras theorem]

With O as centre and OC as radius, draw an arc, meeting at point Q on the number line.

Then, OQ = OC = √6.

Thus, Q represents √6 on the real line.