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Construct a Square Root Spiral Experiment Class 9 Maths Practical NCERT

The experiment to determine Construct a Square Root Spiral are part of the Class 9 Maths Lab Manual provides practical activities and experiments to help students understand mathematical concepts effectively. It encourages interactive learning by linking theoretical knowledge to real-life applications, making mathematics enjoyable and meaningful.

Maths Lab Manual Class 9 CBSE Construct a Square Root Spiral Experiment

Determine Construct a Square Root Spiral Class 9 Practical

OBJECTIVE

To construct a square root spiral.

Materials Required

  1. Adhesive
  2. Geometry box
  3. Marker
  4. A piece of plywood

Prerequisite Knowledge

  1. Concept of number line.
  2. Concept of irrational numbers.
  3. Pythagoras theorem.

Theory

  1. A number line is a imaginary line whose each point represents a real number.
  2. The numbers which cannot be expressed in the form p/q where q ≠ 0 and both p and q are integers, are called irrational numbers, e.g. √3, π, etc.
  3. According to Pythagoras theorem, in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of other two sides containing right angle. ΔABC is a right angled triangle having right angle at B. (see Fig. 1.1)NCERT Class 9 Maths Lab Manual - Construct a Square Root Spiral 1
  4. Therefore, AC² = AB² +BC²
    where, AC = hypotenuse, AB = perpendicular and BC = base

Procedure

  1. Take a piece of plywood having the dimensions 30 cm x 30 cm.
  2. Draw a line segment PQ of length 1 unit by taking 2 cm as 1 unit, (see Fig. 1.2)
    NCERT Class 9 Maths Lab Manual - Construct a Square Root Spiral 2
  3. Construct a line QX perpendicular to the line segment PQ, by using compasses or a set square, (see Fig. 1.3)NCERT Class 9 Maths Lab Manual - Construct a Square Root Spiral 3
  4. From Q, draw an arc of 1 unit, which cut QX at C(say). (see Fig. 1.4)
    NCERT Class 9 Maths Lab Manual - Construct a Square Root Spiral 4
  5. Join PC.
  6. Taking PC as base, draw a perpendicular CY to PC, by using compasses or a set square.
  7. From C, draw an arc of 1 unit, which cut CY at D (say).
  8. Join PD. (see Fig. 1.5)
    NCERT Class 9 Maths Lab Manual - Construct a Square Root Spiral 5
  9. Taking PD as base, draw a perpendicular DZ to PD, by using compasses or a set square.
  10. From D, draw an arc of 1 unit, which cut DZ at E (say).
  11. Join PE. (see Fig. 1.5)

Keep repeating the above process for sufficient number of times. Then, the figure so obtained is called a ‘square root spiral’.

Demonstration

  1. In the Fig. 1.5, ΔPQC is a right angled triangle.
    So, from Pythagoras theorem,
    we have PC² = PQ² + QC²
    [∴ (Hypotenuse)² = (Perpendicular)² + (Base)²]
    = 1² +1² =2
    => PC = √2
    Again, ΔPCD is also a right angled triangle.
    So, from Pythagoras theorem,
    PD² =PC² +CD²
    = (√2)² +(1)² =2+1 = 3
    => PD = √3
  2. Similarly, we will have
    PE= √4
    => PF=√5
    => PG = √6 and so on.

Observations
On actual measurement, we get
PC = …….. ,
PD = …….. ,
PE = …….. ,
PF = …….. ,
PG = …….. ,
√2 = PC = …. (approx.)
√3 = PD = …. (approx.)
√4 = PE = …. (approx.)
√5 = PF = …. (approx.)

Result
A square root spiral has been constructed.

Application
With the help of explained activity, existence of irrational numbers can be illustrated.

Viva Voce
Question 1:
Define a rational number.
Answer:
A number which can be expressed in the form of p/q, where q ≠ 0 and p, q are integers, is called a rational number.

Question 2:
Define an irrational number.
Answer:
A number which cannot be expressed in the form of p/q, where q ≠ 0 and p, q are integers, is called an irrational number.

Question 3:
Define a real number.
Answer:
A number which may be either rational or irrational is called a real number.

Question 4:
How many rational and irrational numbers lie between any two real numbers?
Answer:
There are infinite rational and irrational numbers lie between any two real numbers.

Question 5:
Is it possible to represent irrational numbers on the number line?
Answer:
Yes, as we know that each point on the number line represent a real number (i.e. both rational and irrational), so irrational number can be represented on number line.

Question 6:
In which triangle, Pythagoras theorem is applicable?
Answer:
Right angled triangle

Question 7:
Give some examples of irrational numbers.
Answer:
Some examples of irrational numbers are √5, 3 – √7,2π, etc.

Question 8:
Can we represent the reciprocal of zero on the number line.
Answer:
No, because reciprocal of zero is undefined term, so we cannot represent on number line.

Question 9:
In a square root spiral, is it true that in each square root of natural number is equal to the square root of the sum of 1 and previous natural number (> 1)?
Answer:
Yes

Question 10:
Is it possible that we make a square root spiral of negative nymbers?
Answer:
No

Suggested Activity
Represent square root of 7 and 9 by constructing a square root spiral.

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NCERT Class 9 Maths Lab Manual