Q1: State whether true or false. Justify answers.
(सत्य या असत्य बताइए और कारण दीजिए।)

1. Every irrational number is a real number.
   True (सत्य): Real numbers are the collection of both rational and irrational numbers.
2. Every point on the number line is of the form √m, where m is a natural number.
   False (असत्य): Negative numbers exist on the number line, but the square root of a natural number is never negative.
3. Every real number is an irrational number.
   False (असत्य): Real numbers include rational numbers too (e.g., 2 is real but not irrational).

Q2: Are the square roots of all positive integers irrational? Give an example if not.
(क्या सभी धनात्मक पूर्णांकों के वर्गमूल अपरिमेय होते हैं? यदि नहीं, तो उदाहरण दीजिए।)

Solution (हल):
No (नहीं). For example, √4 = 2. Here, 2 is a rational number.

Q3: Show how √5 can be represented on the number line.
(दिखाइए कि संख्या रेखा पर √5 को किस प्रकार निरूपित किया जा सकता है।)

Solution (हल):
By Pythagoras theorem, 5 = (2)² + (1)².
1. Draw a number line and mark point A at 2 units from 0 (OA = 2).
2. Draw a perpendicular AB of 1 unit at A.
3. Join OB. The length of OB = √(2² + 1²) = √5.
4. With O as center and OB as radius, draw an arc cutting the number line at P. Point P represents √5.