Question

2.
(ii) Every real number is an irrational number.
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.
3.
Show how 5 can be represented on the number line.​

Answer 1

Answer:

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

Step-by-step explanation:

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.

OE=√OD2+DE2OE=OD2+DE2

Or, OE=√22+12OE=22+12

Answer 2

Answer:

2

No, the square roots of all positive integers are not irrational. Because we know that the square roots of all positive integers includes both rational and irrational numbers.

for Example 4, 9, 16, etc. are positive integers and their square roots are 2, 9 and 4 which are rational numbers.

Step-by-step explanation: