(i) We have

 x² = 5

Taking square root on both sides.

=> √x² = √5

=> x = √5

√5 is not a perfect square root, so it is an irrational number. 

(ii) We have

   y² = 9

  => y = √9

  =3

 =3/1

√9 can be expressed in the form of p/q, so it a rational number.

(iii) We have

   z² = 0.04

  Taking square root on both sides, we get,

√z² =√0.04

=> z = √0.04

= 0.2

= 2/10

= 1/5

z can be expressed in the form of p/q, so it is a rational number.

(iv) We have

 u² =17/4

Taking square root on both sides, we get,

√u² =√17/4

=> u = √17/2

Quotient of an irrational and a rational number is irrational, so u is an irrational number.

(v) We have

  v² = 3

 Taking square root on both sides, we get,

√v² = √13

=> v = √3

√3 is not a perfect square root, so y is an irrational number.

(vi) We have

  w² = 27

 Taking square root on both sides, we get,

 √w²  = √27

 => w = √3 x 3 x 3

 =3√3

 Product of a rational and an irrational is irrational number, so w is an irrational number. 

(vii) We have

  t² = 0.4

 Taking square root on both sides, we get

 √t² = √0.4

 => t = √4/10

 = 2/√10

Since, quotient of a rational and an irrational number is irrational number, so t is an irrational number.