Question

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Answer 1

Answer- The given questions are from the chapter 'Number system'.

Rational Numbers- Numbers which can be written in the form of p/q where p,q are integers and q ≠ 0.

Decimal expansion of rational numbers is always terminating or non-terminating but repeating.

Example: 0, 2/3, -4/7, 2.1212..., etc.

Irrational Numbers- Numbers which can't be written in the form of p/q.

Decimal expansion of irrational numbers is always non-terminating non- repeating.

Example: π, √3, √7, 2.343443444..., etc.

Question: Examine whether the following numbers are rational or irrational.

Solution:

i) (3 + √3) + (3 - √3)

= 3 + √3 + 3 - √3

= 3 + 3

= 6 which is a rational number

ii) (3 + √3) (3 - √3)

= 3² - (√3)²

= 9 - 3

= 6 which is a rational number

iii) 10/√2

= 10/√2 × √2/ √2

= 10√2/2 which is an irrational number

iv) (√2 + 2)²

= (√2)² + 2² + 2.√2.2

= 2 + 4 + 4√2

= 6 + 4√2 which is an irrational number

Answer 2

Answer:

1. Rational number
2. rational number
3. irrational number
4. irrational number

Step-by-step explanation:

(i)3+√3+3-√3=6+√3-√3=6

THIS IS A RATIONAL NUMBER

(ii)3+√3(3-√3)=3^2-(√3)^2=9-3=6

THIS IS A RATIONAL NUMBER.

(iii)10/2√5=5/√5=√5*√5/√5=√5

THIS IS AN IRRATIONAL NUMBER.

(iv)(2+√2)^2=2^2+(√2)^2+2*2*√2

=4+2+4√2=6+4√2

THIS IS AN IRRATIONAL NUMBER.

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