Let us write rational and irrational numbers from the following:

(i) √9 (ii) √225

(iii) √7 (iv) √50

(v) √100 (vi) -√81

(vii) √42 (viii) √29

(ix) -√1000

(i) As we know 9 is a square of 3,

⇒ √9 = 3, which is rational

∴ √9 is a rational number.

(ii) As we know 225 is a square of 15,

⇒ √225 = 15, which is a rational number

∴ √225 is a rational number.

(iii) As value of √7 cannot be written exactly and thereby cannot be written in form, √7 is an irrational number.

(iv) We can write,

√50 = 5√2

As value of √2 cannot be written exactly and thereby cannot be written in form, √2 is an irrational number.

∴ √50 is an irrational number.

(v) As we know 100 is a square of 10,

⇒ √100 = 10, which is a rational number

∴ √100 is a rational number.

(vi) As we know 81 is a square of 9,

⇒ -√100 = -9 , which is a rational number

∴ -√81 is a rational number.

(vii) As value of √42 cannot be written exactly and thereby cannot be written in form, √42 is an irrational number.

(viii) As value of √29 cannot be written exactly and thereby cannot be written in form, √29 is an irrational number.

(ix) We can write,

-√1000 = -10√10

As value of √10 cannot be written exactly and thereby cannot be written in form, √10 is an irrational number.

∴ -√1000 is an irrational number.