**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 = √(1^{2} +1^{2}). 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**

- (i)
- (i)
- (ii)
- (iii)
- (ii)
- (i)
- (i)
- (iii)
- (ii)
- (ii)

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