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Question

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=174

(v) v2 = 3 (vi) w2= 27

(vii) t2=0.4

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Solution

(i) x2 = 5 x2 = ±5)2

x = 5

Which is an irrational number.

(ii) y2= 9 y2 = (3) 2

y = 3

(iii) z2 = 0.04 (0.2)2

z = 0.2

Which is a rational number.

(iv) u2=174=(172)2 u= 172

Which is an irrational number.

(v) v2=3=(3)2

Which is an irrational number.

(vi) w2=27 9×3=(33)2

w = 33

Which is an irrational number.

(vii) t2=0.4t2=410=(210)2=210=2×1010×10=21010=105


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