• Skip to main content
  • Skip to primary sidebar
  • Skip to footer
  • NCERT Solutions
    • NCERT Solutions for Class 12 English Flamingo and Vistas
    • NCERT Solutions for Class 11 English
    • NCERT Solutions for Class 11 Hindi
    • NCERT Solutions for Class 12 Hindi
    • NCERT Books Free Download
  • TS Grewal
    • TS Grewal Class 12 Accountancy Solutions
    • TS Grewal Class 11 Accountancy Solutions
  • CBSE Sample Papers
  • NCERT Exemplar Problems
  • English Grammar
    • Wordfeud Cheat
  • MCQ Questions

CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

NCERT Class 9 Maths Lab Manual – Construct a Square Root Spiral

NCERT Class 9 Maths Lab Manual – Construct a Square Root Spiral

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.

Math LabsMath Labs with ActivityMath Lab ManualScience LabsScience Practical Skills

Primary Sidebar

NCERT Exemplar problems With Solutions CBSE Previous Year Questions with Solutoins CBSE Sample Papers
  • The Summer Of The Beautiful White Horse Answers
  • Job Application Letter class 12 Samples
  • Science Lab Manual Class 9
  • Letter to The Editor Class 12 Samples
  • Unseen Passage For Class 6 Answers
  • NCERT Solutions for Class 12 Hindi Core
  • Invitation and Replies Class 12 Examples
  • Advertisement Writing Class 11 Examples
  • Lab Manual Class 10 Science

Recent Posts

  • Pressure of a Liquid : Definition, Units and Solved Examples
  • Specific Gravity : Definition, Equation and Solved Examples
  • Omission Exercises for Class 9 CBSE with Answers
  • Stress-Strain Graph : Load-Extension Graph of a String
  • Force Constant of Spring : Series and Parallel Combination
  • Work Done in Stretching a Wire : Energy Density
  • Poisson’s Ratio : Longitudinal and Lateral Strain
  • Mother’s Day Class 11 Questions And Answers NCERT
  • Albert Einstein At School Class 11 Questions And Answers NCERT
  • Elastic Moduli: Young’s Modulus, Shear Modulus, Formula and Units
  • Ranga’s Marriage Class 11 Questions And Answers NCERT
  • The Address Class 11 Questions And Answers NCERT
  • The Summer Of The Beautiful White Horse Class 11 Questions And Answers NCERT
  • Elastic Property of Matter : Some Useful Definitions
  • What is Weightlessness in Artificial Satellite With Example?

Footer

Maths NCERT Solutions

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 11 Maths
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 8 Maths
NCERT Solutions for Class 7 Maths
NCERT Solutions for Class 6 Maths

SCIENCE NCERT SOLUTIONS

NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Chemistry
NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 9 Science
NCERT Solutions for Class 7 Science
MCQ Questions NCERT Solutions
CBSE Sample Papers
NCERT Exemplar Solutions LCM and GCF Calculator
TS Grewal Accountancy Class 12 Solutions
TS Grewal Accountancy Class 11 Solutions