Are the square root of all the positive integers irrational? If yes, then explain in about 50-60 words
Answers
Step-by-step explanation:
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.
Question 3: Show how √5 can be represented on the number line.
Answer: class nine math number system 45
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, acaccording to Pythagoras theorem.
O
E
=
√
O
D
2
+
D
E
2
Or,
O
E
=
√
2
2
+
1
2
Or,
O
E
=
√
4
+
1
..