Number System EXERCISE 1.2

EXERCISE 1.2

Question – 1 – State whether the following statements are true or false. Justify your answers.

(i) Every irrational number is a real number.

(ii) Every point on the number line is of the form √m , where m is a natural number.

(iii) Every real number is an irrational number.

Answer –

(i) True

Justification – Real numbers are any number which can we think. Thus, every irrational number is a real number.

(ii) False

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

(iii) False

Justification – 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.

Question – 2 – Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

Answer – No. Square roots of all positive integers are not irrational. Example 4, 9, 16, etc. are is a positive integers and their square roots are 2, 9 and 4 are rational numbers.

Question – 3 – Show how √5 class nine math number system 35 can be represented on the number line.

Answer –

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.