How To Draw Square Root Spiral On A Number Line

CBSE Class 9 Maths Lab Manual – Square Root Spiral

Objective
To make a square root spiral by using paper folding.

Prerequisite Knowledge
In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
eg., √2 = √(1² +1²). By using this Concept, we will represent irrational numbers on a number line by paper folding.

Materials Required
Tracing paper, pencil, geometry box.

Procedure
To represent √2 on a number line.

Draw a line OX on the tracing paper. Mark point O on one end and mark points 0, 1,2, 3, … at equal distances of 1 unit by paper folding.
Fold the paper along the line that passes through the point marked '1' and perpendicular to the line OX, i.e., fold the paper in such a way that point 'O' coincides with point '2'. Make a crease and unfold it. From the point marked '1', draw a line of length 1 unit moving along the crease. Mark the point as M such that PM = 1 unit. Join OM, clearly OM= √2 units.
Fold the paper along the line ( fold on point M in such a way that point O joined with any point lie on OX,) that passes through point M and perpendicular to OM at M. Make a crease and unfold it. From the point M, draw a line of 1 unit moving upward, along the crease. Mark the point as N such that MN = 1 unit. Join ON, where ON = √3.
Keep this process continuously to get √4, √5, √6, ……….

Result
In this way, we get a square root spiral pattern by using paper folding.

Learning Outcome
On the same plane, different irrational numbers can be represented on the number line by paper folding method.
By using Pythagora's theorem students will be able to construct a square root spiral by paper folding method.

Activity Time
Students can construct a square root spiral by paper folding using different coloured glazed papers for each triangle so formed.

Viva Voce

Question 1.
Is it possible to represent irrational numbers on the number line ?
Answer:
Yes.

Question 2.
What do you mean by irrational numbers?
Answer:
Decimal expansion of irrational numbers is non-terminating and non-recurring.

Question 3.
Give one example of irrational number.
Answer:
1.0010011000111000001111 …………, √3, √5, π

Question 4.
Which theorem is used to represent irrational numbers on the number line ?
Answer:
Pythagoras' theorem.

Question 5.
In which triangle, Pythagoras' theorem is applicable ?
Answer:
Right-angled triangle.

Question 6.
What do you mean by Pythagorean triplets ?
Answer:
Three numbers which satisfy the Pythagoras' theorem, i.e., the sum of squares of two numbers is equal to square of the third number.

Question 7.
Is 2/0 a rational number?
Answer:
No, here denominator is zero.

Question 8.
Is \(\sqrt [ 3 ]{ 7 }\) a rational or an irrational number ?
Answer:
\(\sqrt [ 3 ]{ 7 }\) is an irrational number

Question 9.
Are all irrational numbers, real numbers ?
Answer:
Yes.

Question 10.
Are all integers, whole numbers ?
Answer:
No, only zero and all positive integers are whole numbers.

Multiple Choice Questions

Question 1.
Evaluate √4 :
(i) 2
(ii) 3
(iii) 16
(iv) none of these

Question 2.
The square root of 5 is:
(i) an irrational number
(ii) a rational number
(iii) an integer
(iv) none of these

Question 3.
The mixed surd of √20 is :
(i) √5
(ii) 2√5
(iii) 74
(iv) none of these

Question 4.
The rationalizing factor of √23 is:
(i) 24
(ii) 23
(iii) √23
(iv) none of these

Question 5.
The rationalizing factor of 2√2 is:
(i) 8
(ii) √2
(iii) 2√2
(iv) none of these

Question 6.
The rationalizing factor of 3 + √5 is:
(i) 3 – √5
(ii) -3 – √5
(iii) √5
(iv) none of these

Question 7.
The sum of 2 + √7 and 2 – √7 is:
(i) 4
(ii) 0
(iii) 2√7
(iv) none of these

Question 8.
The product of 3√5 and 3√6 is :
(i) √30
(ii) 6√30
(iii) 9√30
(iv) none of these

Question 9.
The Pythagorean triplets for √2 is:
(i) 1, √2, 3
(ii) 1, 1, √2
(iii) √2, 1, √2
(iv) none of these

Question 10.
The set or collection of rational numbers and irrational numbers is known as :
(i) integers
(ii) real numbers
(iii) whole numbers
(iv) none of these

Answers