Q1: Classify the following numbers as rational or irrational.
(बताइए नीचे दी गई संख्याओं में कौन-कौन परिमेय हैं और कौन-कौन अपरिमेय हैं।)

(i) 2 - √5 ⇒ Irrational (अपरिमेय) - Because subtracting an irrational from a rational gives an irrational.
(ii) (3 + √23) - √23 ⇒ 3 + √23 - √23 = 3 ⇒ Rational (परिमेय)
(iii) 2π ⇒ Irrational (अपरिमेय) - Because π is irrational.

Q2: Simplify each of the following expressions.
(निम्नलिखित व्यंजकों में से प्रत्येक को सरल कीजिए।)

(i) (3 + √3)(2 + √2)
= 3(2 + √2) + √3(2 + √2)
= 6 + 3√2 + 2√3 + √6

(ii) (5 + √5)(5 - √5)
Using formula (a+b)(a-b) = a² - b²
= (5)² - (√5)² = 25 - 5 = 20

Q5: Rationalize the denominators of the following.
(निम्नलिखित के हरों का परिमेयकरण कीजिए।)

(i) 1 / √7
Multiply numerator and denominator by √7:
= (1 × √7) / (√7 × √7) = √7 / 7

(ii) 1 / (√7 - √6)
Multiply by the conjugate (√7 + √6):
= [1 × (√7 + √6)] / [(√7 - √6)(√7 + √6)]
= (√7 + √6) / (7 - 6) = √7 + √6