Quisque velit nisi, pretium ut lacinia in, elementum id enim. Praesent sapien massa, convallis a pellentesque nec, egestas non nisi. Curabitur aliquet quam id dui posuere blandit. Donec rutrum congue leo eget malesuada. Vivamus magna justo, lacinia eget consectetur sed, convallis at tellus. Cras ultricies ligula sed magna dictum porta. Vivamus suscipit tortor eget felis porttitor volutpat. Nulla quis lorem ut libero malesuada feugiat. Vestibulum ante ipsum primis in faucibus orci luctus ultrices posuere cubilia Curae; Donec velit neque, auctor sit amet aliquam vel, ullamcorper sit amet ligula. Curabitur aliquet quam id dui posuere blandit.
Donec sollicitudin molestie malesuada. Cras ultricies ligula sed magna dictum porta. Curabitur arcu erat, accumsan id imperdiet et, porttitor at sem. Curabitur non nulla sit amet nisl tempus convallis quis ac lectus. Vivamus suscipit tortor felis porttitor volutpat. Curabitur non nulla sit amet nisl tempus convallis quis ac lectus. Proin eget tortor risus. Vivamus suscipit tortor eget felis porttitor volutpat.
Requirements
Donec sollicitudin molestie malesuada. Cras ultricies ligula sed magna dictum porta. Curabitur arcu erat, accumsan id imperdiet et, porttitor at sem. Curabitur non nulla sit amet nisl tempus convallis quis ac lectus. Vivamus suscipit tortor felis porttitor volutpat. Curabitur non nulla sit amet nisl tempus convallis quis ac lectus. Proin eget tortor risus. Vivamus suscipit tortor eget felis porttitor volutpat.
- Praesent sapien massa, convallis a pellentesque nec, egestas non nisi.
- Curabitur aliquet quam id dui posuere blandit.
- Vivamus magna justo, lacinia eget consectetur sed, convallis at tellus.
What you'll learn
Quisque velit nisi, pretium ut lacinia in, elementum id enim. Praesent sapien massa, convallis a pellentesque nec, egestas non nisi. Curabitur aliquet quam id dui posuere blandit. Donec rutrum congue leo eget malesuada. Vivamus magna justo, lacinia eget consectetur sed, convallis at tellus.
Donec sollicitudin molestie malesuada. Cras ultricies ligula sed magna dictum porta. Vivamus suscipit tortor eget felis porttitor volutpat. Nulla quis lorem ut libero malesuada feugiat. Vestibulum ante ipsum primis in faucibus orci luctus ultrices posuere cubilia Curae; Donec velit neque, auctor sit amet aliquam vel, ullamcorper sit amet ligula. Curabitur aliquet quam id dui posuere blandit.
- Teacher: John Smith
We know that a real number is either rational or irrational. So, we can say that every real number is represented by a unique point on the number line.
Also, every point on the number line represents a unique real number. So, we can locate some of the irrational number of the form \( \sqrt[2]{n} \) , where n is a positive integer on the number line by using following steps.
Step | - Write the given number (without root) as the sum of the squares of two natural numbers (say a and b, where a > b).
Step Il - Take the distance equal to these two natural numbers on the number line (a on number line and b vertically) starting from 0 (say OA and AB) in such a way that one is perpendicular to other (say AB 1 OA).
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Demonstration
1. With the help of screw, fix the perpendicular wooden strip at 1, which is 1 unit on horizontal scale.
2. Tie the other end of the thread to unit 1 on the perpendicular strip.
3. Remove the thread from unit 1 on the perpendicular strip and place it on the horizontal strip to represent 2 on the horizontal strip.
AOAB is a right angled triangle.
So, from Pythagoras theorem, OB? = OA? + АВ=
Here, OA = 1 unit, AB = 1 unit,
OB? = (1)2 + (1)2=> OB? =2 => OB = /2 Similarly, to represent V3, fix the
perpendicular wooden strip at 2 and repeat the above process.
Thus, we conclude to represent va, a > 1 fix the perpendicular scale at Va - 1 and proceed as above to get va.
Note: To find Va such as V13 by fixing the perpendicular strip at 3 on the horizontal strip and tying the other end of thread at 2 on the vertical strip.
Observation
On actual measurement, we get a -1 = ....
Result
Any irrational number can be represented on the number line by using this method.
Application
This activity may help to student in representing some irrational numbers like v2, V3, V5, V6, 17,
...., etc., on the number line.
Viva Voce
Question 1:
Is every irrational number, a real number?
Answer:
Yes, because real numbers consist of both rational and irrational numbers.
Question 2:
Can we apply Pythagoras theorem in any triangle?
Answer:
No, Pythagoras theorem is applicable only in right angled triangle.
Question 3:
Isrca rational or an irrational number? What is value of TC up to three decimal places?
Answer:
T is an irrational number. The value of t is 3.142.
- Teacher: John Smith
- Teacher: John Smith
