CBSE Class 9 Maths Lab Manual – An Irrational Number

CBSE Class 9 Maths Lab Manual – An Irrational Number

Objective
To represent an irrational number on the number line. (To represent √2 on number line).

Prerequisite Knowledge
Concept of Pythagoras theorem:
In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides containing right angle.
In a right angled triangle, if the base and perpendicular are of 1 unit each, the hypotenuse will be
√(1² +1²) = √2.
Now, by using this concept, we will represent √2 on the number line.

Materials Required
A sheet of white paper, pencil, compass, eraser and ruler etc.

Procedure

1. Draw a straight line X’OX on the white sheet of paper.
2. Divide that line into equal parts from point O by paper folding activity taking each part as 1 unit. Mark the points as 1,2,3,…. etc.
3. Draw the perpendicular at the point marked as ‘1’ by paper folding.
4. Unfold the paper, and draw the line at the crease so formed. Mark a point A on this crease at 1 unit from line X’OX.
   
   
5. Join O and A, we get OA = √2 units (By Pythagoras theorem).
6. With O as centre, OA as radius, draw an arc intersecting the line X’OX at M.

Observation
We observe that OA = OM = √2 units.

Result
An irrational number √2 is represented on the number line.

Learning Outcome
Students can represent any irrational number on number line by using above method.
e.g., (√3)² = (√2)² +(1)²
At M, by paper folding draw perpendicular BM on the number line of 1 unit. Join OB. With O as centre and OB as radius draw an arc intersecting the line at N.
Thus OB = ON = √3 on the number line.

Activity Time
Represent √5, √7 on the number line.

Viva Voce

Question 1.
What are real numbers ?
Answer:
The collection of all rational numbers and irrational numbers.

Question 2.
What do you mean by rational and irrational numbers ?
Answer:
Decimal expansion of rational numbers are either terminating or recurring. Irrational numbers are non-terminating and non-recurring.

Question 3.
Is π a rational number ?
Answer:
No, π is an irrational number.

Question 4.
Can the sum of two irrational numbers be zero ?
Answer:
Yes, e.g., (2 + √2)+ (-√2 – 2) = 0

Question 5.
Can the square root of any natural number be negative ?
Answer:
No

Question 6.
Is the square root of -5 is real ?
Answer:
No.

Question 7.
Write √45 in mixed surd ?
Answer:
3√5.

Question 8.
What do you mean by surd ?
Answer:
If the positive nth root of a number is an irrational number it is called a surd or radical.

Question 9.
Who showed that corresponding to every real number, there is a point on the real number line and corresponding to every point on the number line, there exists a real number ?
Answer:
Two German Mathematicians named as Centor and Dedekind.

Multiple Choice Questions

Question 1:
Irrational numbers are:
(i) terminating decimals.
(ii) non-terminating and non-recurring decimals.
(iii) non-recurring decimals.
(iii) none of these.

Question 2:
Who discovered Pythagoras’ theorem ?
(i) Pythagoras
(ii) Issac Newton
(iii) Euclid
(iv) none of these

Question 3:
In which triangle, the Pythagoras’ theorem is applicable ?
(i) right triangle
(ii) obtuse triangle
(iii) acute triangle
(iv) none of these .

Question 4:
Without actual division, check whether \(\frac { 47 }{ 14 }\) is terminating or not:
(i) terminating
(ii) non-terminating
(iii) irrational
(iv) none of these

Question 5:
Write the Pythagorean triplets for √2:
(i) (√2, 1, 1)
(ii) (1, √2, 3)
(iii) (1, 1, 3)
(iv) none of these

Question 6:
Write the Pythagorean triplets for √5:
(i) (√2, 1, √3)
(ii) (√5, √2, 1)
(iii) (√5, √4, 1)
(iv) none of these

Question 7:
Give one example each of rational number and irrational number:
(i) √8, √10
(ii) √2, √6
(iii) √4, √2
(iv) none of these

Question 8:
The product of’ a rational number and an irrational number is always:
(i) a rational number
(ii) an irrational number
(iii) an integer
(iv) none of these

Question 9:
Is \(\frac { 3 }{ 20 }\) an irrational number?
(i) no
(ii) yes
(iii) not real number
(iv) none of these

Question 10:
Two irrational numbers whose sum is a rational are:
(i) √2 and √3
(ii) √2 and (-√2)
(iii) √3and (√3 – √5)
(iv) none of these

Answers

1. (ii)
2. (i)
3. (i)
4. (ii)
5. (i)
6. (iii)
7. (iii)
8. (ii)
9. (i)
10. (ii)

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