Question

locate root 2 on number line

Answer 1

) Initially mark a horizontal line, let it be number line. Mark a point O on it; then mark OA one unit on this line. ii) At O erect a perpendicular to the number line; here again mark OB equals one unit. iii) Join AB; with A as center and AB as radius mark cut off an arc on the number line at C. So AC equals √2. Proof: Since by construction, OAB is a right triangle, with AB as hypotenuse. Applying Pythagoras theorem, AB² = OA² + OB² Each of OA & OB being one unit by construction. AB² = 1 + 1 = 2 ==> AB = √2 units. Thus AC = √2 units.

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.

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.

Therefore, OC = √2.

• You can draw these measures using the above steps.