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**Q.1. Which of the following is an irrational number?(a) **

Ans.

Ans.

let x be the p/q form, x =

multiply both side by 100, 100 x = ...(i)

multiply both side by 10

1000 x = ....(ii)

1000 x - 100 x = = 241

900 x = 241

⇒ x = 241/900

Hence, option (c) is correct

Ans.

Ans.

Let us assume 3√5 is a rational number,

3√5 = p/q, where p and q are co-primes,

√5 = p/3q

Clearly √5 is irrational, while number on right q ≠ 0 are rational

∴ Irrational = Rational

But above deduced can't be right. Therefore our supposition is wrong making 3√5 an irrational number.

= 5+4 - 4√5 - 5 - 4 - 4√5 = -8√5

Rationalising LHS

∴ a = 11/7 and b = 6/7

x = 2 + √3

x

= x(x

= (2 + √3) [(2 + √3)

= (2 + √3) [4 + 3+4√3 - 4 + 2√3 - 7]+5

= (2 + √3)(-4 + 2√3) + 5

= (2 + √3) x 2(-2+√3)+5

= 2[(√3 + 2)(√3 - 2)] + 5

= 2[(√3)

= 2[3-4]+5

= 2(-1) + 5

= -2+5

= 3

let x be the p/q form,

so, x =

10x =

1000x =

1000x - 10x = -

990x = 15555

x= 15555/990

= 1037/66

3/5 and 4/5

30/50 and 40/50

∴ pick any five number between 30 and 40

31/50, 32/50, 36/50, 37/50, 39/50

2.6 and 3.8

irrational numbers are non repeating non - terminating

2.61010010001.....

2.802002000200002......

3.604004000400004.......

27

⇒ 3

⇒ 3

⇒ 3x = 2-x

⇒ 4x = 2

⇒ x = 4/2

⇒ x = 0.5

= 15

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