Question

Pls explain each part of Q3 in detail

Answer 1

Q.3) (i) √7 is an irrational number
Reason:- Value under root is prime.

(ii) √4 is a rational number
Reason:- Value under root can be broken into product of two primes (i.e. 2*2)

(iii) 2+√3 is an irrational number
Reason:- Sum of a rational number and an irrational number is always irrational

(iv) √3+√3 is an irrational number
Reason:- Sum of two irrational number is always irrational

(v) √3+√5 is an irrational number
Reason:- Same as no. (iv)

(vi) (√2-2)² is an irrational number
Reason:- On breaking the square, we get:- 2+4-2*√2*2= 6-4√2

(vii) (2-√2)(2+√2) is a rational number
Reason:- On breaking the brackets, we get:- 4+2√2-2√2-2= 2

(viii) (√2+√3)² is an irrational number
Reason:- On breaking the square, we get:- 2+3+2√6= 5+2√6

(ix) √5-2 is an irrational number
Reason:- Difference of a rational from an irrational is always irrational

(x) √23 is an irrational number
Reason:- Value under root is prime

(xi) √225 is a rational number
Reason:- Value under root can be broken into the product of two natural number (i.e. 15*15)

(xii) 0.3796 is a rational number
Reason:- Value given is a terminating decimal (i.e. terminates at 6)

(xiii) 7.478478.... is a rational number
Reason:- Value given is a a non-terminating repeating decimal (i.e. repeats after 8)

(xiv) 1.1010010001...is an irrational number
Reason:- Value given is a non-terminating non-repeating decimal

Hope this helps you!