source: ncert_exercises
topic: numbers
class_level: class_9
chapter: ch1
exercise: ex1.2
difficulty: beginner
Class 9 | Ch1: Number Systems | Exercise 1.2
Q1. State whether true or false. Justify. (i) Every irrational number is a real number. (ii) Every point on the number line is of the form √m where m is a natural number. (iii) Every real number is an irrational number. Answer: (i) TRUE — Real = rational + irrational. (ii) FALSE — Points like -3, 0.5 cannot be written as √m. (iii) FALSE — Rational numbers like 2, 1/2 are real but NOT irrational. ✅ (i)True (ii)False (iii)False.
Q2. Are square roots of all positive integers irrational? Give example. Answer: NO. √4 = 2 is rational. √9 = 3 is rational. ✅ Not all square roots are irrational.
Q3. Show how √5 can be represented on the number line. Answer: Mark O at 0, A at 2. Draw AB ⊥ OA at A with AB=1. Join OB = √(4+1) = √5. With O as centre, OB as radius, draw arc cutting number line at P. ✅ P represents √5.
Q4. Classroom activity — construct the square root spiral. Answer: Start at O. Draw OA₁=1. A₁A₂ ⊥ OA₁=1. OA₂=√2. A₂A₃ ⊥ OA₂=1. OA₃=√3. Continue → gives √2, √3, √4, √5... ✅