Question

represent √5 on number line​

Answer 1

♡ Heya buddy ♡

⚫Follow these steps :-

1. Draw number line as shown in the figure. Let the point O represent 0(zero) and point A represents

2. Draw perpendicular AX at A on the number line and cut-off arc AB=1unit.

2. Draw perpendicular AX at A on the number line and cut-off arc AB=1unit.We have OA=2 units and AB=1unit.

Using pythagoras theorem, we have,

OB^2 = OA^2 + AB^2

➱OB^2 = 2^2 +1^2

➱OB =√5

Taking O as the centre and OB= √5 as radius draw an arc cutting real line at C.

Clearly, OC=OB= √5

Hence, C represents √5 on the number line.

✧ Thanks ✧

Answer 2

Answer:

Step-by-step explanation:

If possible, let √5 be rational and let's it's simplest form a/b.

√5=a/b

5=a²/b²

5b²=a²

5 divides a² ( 5 divides 5b²)

5divides a

Now,

Let a=5c for some integer c.

Putting a=5c in (i), equation

We get,

5b²=25c²

b²=5c²

5 divides b² ( 5 divides 5c²)

5 divides b

5 is a common factor of a and b.

The contradiction arises by assuming that √5 is rational

Hence, √5 is irrational.

I hope you understand