Question

Show how root 2, root 3, root 5, root 8, can be represented in singlebnumber line

Answer 1

Answer:

Step-by-step explanation:

To represent 3–√on the number line, first of all we have to represent 2–√ on the number line. The procedure for the representation of 2–√ will be same in the previous example. So, let’s start from there only. The steps further followed will be as:

Step I: Now we need to construct a line which is perpendicular to line AB from point A such that this new line has unity length and let’s name the new line as AE.

Step II: Now join (C) and (E). The length of line CE could be found out by using Pythagoras theorem in right angled triangle EAC. So;

    AE2 + AC2 = EC2

⟹ EC2 = 12 + (2–√)2

⟹ EC2 = 1 + 2

⟹ EC2 = 3

⟹ EC = 3–√

So the length of EC line is found to be 3–√ units.

Step III: Now, with (C) as center and EC as the radius of circle cut an arc on the number line and mark the point as F. Since, OE is the radius of the arc, hence OF will also be the radius of the arc and will have the same length as that of OE. So, OF = 3–√ units. Hence, F will represent 3–√ on the number line.

Similarly, we can represent any rational number on the number line.

plz mark as brainliest