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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

â‡’ x = 241/900

Hence, option (c) is correct

Ans.

Ans.

Let us assume 3âˆš5 is a rational number,

3âˆš5 = p/q, where p and q are co-primes,

âˆš5 = p/3q

Clearly âˆš5 is irrational, while number on right q â‰ 0 are rational

âˆ´ Irrational = Rational

But above deduced can't be right. Therefore our supposition is wrong making 3âˆš5 an irrational number.

= 5+4 - 4âˆš5 - 5 - 4 - 4âˆš5 = -8âˆš5

Rationalising LHS

âˆ´ a = 11/7 and b = 6/7

x = 2 + âˆš3

x

= x(x

= (2 + âˆš3) [(2 + âˆš3)

= (2 + âˆš3) [4 + 3+4âˆš3 - 4 + 2âˆš3 - 7]+5

= (2 + âˆš3)(-4 + 2âˆš3) + 5

= (2 + âˆš3) x 2(-2+âˆš3)+5

= 2[(âˆš3 + 2)(âˆš3 - 2)] + 5

= 2[(âˆš3)

= 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

âˆ´ 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

â‡’ 3

â‡’ 3

â‡’ 3x = 2-x

â‡’ 4x = 2

â‡’ x = 4/2

â‡’ x = 0.5

= 15

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