Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev

Class 9 Mathematics by Full Circle

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Class 9 : Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev

The document Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev is a part of the Class 9 Course Class 9 Mathematics by Full Circle.
All you need of Class 9 at this link: Class 9

 Ques 1: Classify the following numbers as rational or irrational:

Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev

Ans: (i) 2 – Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev 
Since it is a difference of a rational and irrational number,
∴ 2 – Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev is an irrational number.
Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev
We have Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev which is a rational number
Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev is a rational number
Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev

Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev

(iv) Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev
∵The quotient of rational and irrational is an irrational number.
 ∴  Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev  is an irrational number.

( v )2π
∵ 2π = 2 x π = Product of a rational and an irrational (which is an irrational number)
∴ 2π is an irrational number.

REMEMBER
For real numbers a, b, c and d, we have:
Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev
Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev
Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev

Ques 2: Simplify each of the following expressions:

Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev
Ans: (i) (3+ √3)(2+√2) - 2(3 +√3 ) + √2 (3 +√3)
= (2 x 3 + 2√3 ) + (3√2 +√2 x √3 )
= 6 + 2√3 + 3√2 + √6
Thus, (3 +√3 )(2 +√2 ) = 6 + 2√3 + 3√2 +√6
(ii) (3 +√3 )(3 – √3 ) = (3)2 – ( √3)     [∵ (a + b)(a – b) = a2 – b2]
= 32 – 3
= 9 – 3 = 6
∴ (3 + √3 ) (3 – √3 ) = 6.
(iii) ( √5 +√2 )2= (√5 )2 + (√2)2 + 2( √5)(√2)   [∵ (a + b)2 = a2 + b2 + 2ab]

Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev

Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev

(iv) ( √5 – √2 )( √5 + √2) = (√5 )2 – (√2 )2     [∵ (a + b)(a – b) = a2 – b2]
= 5 – 2 = 3
∴ ( √5 – √2 )( √5 + √2) = 3

Ques 3: Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev . This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
Ans: 
When we measure the length of a line with a scale or with any other device, we only get an approximate rational value, i.e. c and d both are irrational.
   Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev is irrational and hence π is irrational. Thus, there is no contradiction in saying that π is irrational.

Ques 4: Rationalise the denominators of the following:

Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev

Ans:

(i)     Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev
(ii)   Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev
Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev

Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev
Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev
(iv)   ∴  
Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev
Ex 1.5 NCERT Solutions - Number System Class 9 Notes | EduRev

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