Question

pl tell the answer of the above question?( question 8 and 9)​

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 8: Give two rational numbers lying between 0.212112111... and 0.232332333... .

Solution: Two rational numbers lying between 0.212112111... and 0.232332333... are 0.222 and 0.223.

Question 9: Find two irrational numbers between √2 and √3.

Solution: Let √2 be x and √3 be y.

One irrational number = √x × √y = √(√2 × √3) = √√6

Now, let x be √√6 and y be √2

Second irrational number = √x × √y = √(√√6 × √2)

∴Two irrational numbers between √2 and √3 are √√6 and √(√√6 × √2).