Question

Locate the given number on the number line and using the number line write down its value till one place of decimal.
√3 is the given no.
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Answer 1

Steps to use :-

→ Draw a number line having points O at 0(zero) , A at a distance of 1 unit distance . and 2 at a point of same distance .

→ From point A , draw a perpendicular distance of 1 unit length upto point B. we can say that AB is also of 1 unit.

→ Join O to B.

Now in Right angle ∆ , using pythagoras theorem , we get,

→ OB² = OA² + AB²

→ OB² = (1)² + (1)²

→ OB² = 1 + 1

→ OB² = 2

Square - root both sides,

→ OB = √2.

→ Now, From point B draw a perpendicular of length 1 unit

to Point C.

→ join the points 0 and C Now.

Again ,using pythagoras theorem in Right ∆OBC now,

→ OC² = OB² + BC²

→ OC² = (√2)² + (1)²

→ OC² = 2 + 1

→ OC² = 3

Square - root both sides,

→ OC = √3.

→ Now, with compus taking radius equal to OC, draw an arc so that it cuts the number line at D.

→ Then the distance OD is √3.

Also,

→ Value of √3 till one place decimal = 1.7

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Note :- In the same way, we can locate √n for any positive integers n, after √(n−1) has been located.