Question

locate root 2 on the number line​

Answer 1

Steps :

• Draw a number line and take point O and A such that (O,A) is 1 unit.

• Draw (A,B) perpendicular to (O, A) making (A,B) equal to 1 unit.

• Join (O,B)

• From ∆OAB =

$\sf{{(OB)}^{2} = {(OA)}^{2} + {(AB)}^{2}}$

$\sf{{(OB)}^{2} = {(1)}^{2} + {(1)}^{2}}$

$\sf{{(OB)}^{2} = 1 + 1}$

$\sf{{(OB)}^{2} = 2}$

Transposing the power of square to other side makes it :

$\sf{OB = \sqrt{2}}$

• Take 'O' as the centre and OB as the radius .

• Draw an arc which cuts the number line at Point D.

• Point D is √2 on number line.

Note that The value of √2 is nearly 1.41 cm

Answer 2

Answer:

1. Firstly let's take a number line.
2. Let 0 be O and 1 be A. OA be the base.
3. Let A - B be the height with 1 unit.
4. AB perpendicular to AO.
5. Let's join O and B.
6. Therefore, now both AB, OB are equal to 1 unit.

Now using Pythagorean theorem:

⇢ OB² = OA² + AB²

⇢ 1² + 1²

⇢ 2

Now, taking square roots on both the sides:

⇢ OB = √2

Now, here OB is equal to √2 but we need this √2 here on number line.

So, now it's time to take the geometric equipments.

1. Take the vertex point on point O.
2. Now cut an arc in OB on the number.
3. The new point on the number like would be C.
4. Taking the arc we can replace the measure of OB to OC on the number line.
5. Therefore, OC = √2.

You can draw these measures using the above steps.