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

(i) x2 = 5

(ii) y2 = 9

(iii) z2 = 0.04

(iv) u2 = 17/14

(v) v2 = 3

(vi) w2 = 27

(vii) t2 = 0.4

1 Answer

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Best answer

(i) x2 = 5 

Taking square root both the sides, 

x = √5 

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

(ii) y2 = 9 

y2 = 9 or y = 3 

3 can be expressed in the form of p/q, such as 3/1, so it a rational number. 

(iii) z2 = 0.04 

z2 = 0.04 

Taking square root both the sides, we get 

z = 0.2 

0.2 can be expressed in the form of p/q such as 2/10, so it is a rational number. 

(iv) u2 = 17/4 

Taking square root both the sides, we get 

u = √17/2

We know that, quotient of an irrational and a rational number is irrational, therefore, u is an Irrational number. 

(v) v2 = 3 

Taking square root both the sides, we get 

v = √3 

Since, √3 is not a perfect square root, so v is irrational number. 

(vi) w2 = 27 

Taking square root both the sides, we get 

w = 3√3 

We know that, the product of a rational and irrational is an irrational number. Therefore, w is an irrational number. 

(vii) t2 = 0.4 

Taking square root both the sides, we get 

t = √(4/10) 

t = 2/√10 

We know that, quotient of a rational and an irrational number is irrational number. Therefore, t is an irrational number.

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