# In the following equations, find which variables x, y, z etc. represent rational or irrational numbers:

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In the following equations, find which variables x, y, z etc. represent rational or irrational numbers:

(i)  x2 = 5

(ii)  y2 = 9

(iii)  z2 = 0.04

(iv)  u2 = 17/ 4

(v)  v2 = 3

(vi) w2 = 27

vii)  t2 = 0.4

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(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

z= 0.04

Taking square root on both sides, we get,

z=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,

u=17/4

=> u = 17/2

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

(v) We have

v= 3

Taking square root on both sides, we get,

v13

=> v = 3

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

(vi) We have

w= 27

Taking square root on both sides, we get,

√w2  27

=> w = 3 x 3 x 3

=33

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

(vii) We have

t= 0.4

Taking square root on both sides, we get

√t0.4

=> t = 4/10

= 2/10

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