Answer:

these are the answers

Step-by-step explanation:

(i) True

Reason: Real numbers are any number which can we think about. Thus, every irrational number is a real number.

(ii) False

Reason: A number line may have negative or positive number. Since, no negative can be the square root of a natural number, thus every point on the number line cannot be in the form of √m, where m is a natural number.

(iii) False

Reason: All numbers are real number and non terminating numbers are irrational number. For example 2, 3, 4, etc. are some example of real numbers and these are not irrational.

QUE 2

Steps to show √5 on a number line.

Step: 1 – Draw a number line mm’

Step: 2 – Take OA equal to one inch, i.e. one unit.

Step: 3 – Draw a perpendicular AB equal to one inch (1 inch) on point A.

Step: 4 – Join OB. This OB will be equal to √2

Step: 5 – Draw a line BC perpendicular to OB on point B equal to OA i.e. one inch.

Step: 6 – Join OC. This OC will be equal to √3

Step: 7 – Draw a line CD equal to OA and perpendicular to OC.

Step: 8 – Join OD. This will be √4 i.e. equal to 2.

Step: 9 – Draw ED equal to 1 inch and perpendicular to OD.

Step: 10 – Join OE. This will be equal to √5

Step: 11 – Cut a line segment OF equal to OE on number line. This line segment OF will be equal to √5

See how, OE is equal to √5

Here, OD = 2, DE = 1 and angle ODE = 90º

Thus, according to Pythagoras theorem.  

O E = √( O D ² + D E ²)

Or,  O E = √ 2 2 + 1 2  

Or,  O E = √ 4 + 1

Or,  O E = √ 5