Question

3. In the following equations, find whether variables x, y, z etc. represent rational or
irrational numbers
i) x² = 7
ii) y2 = 16
iii) Z2 = 0.02
17
vi) 4 = 256
v) w2 = 27
iv) u²​

Answer 1

1) and 5) are rational numbers.

2) , 3) and 4) are irrational numbers.

Step-by-step explanation:

we are given that

1)     y² = 16

⇒     y = ±4 = ±4 / 1

Which can written in p/q form where p and q ∈ Integers and q ≠ 0

SO   y² = 16  is rational number.

2)     z² = 0.02 = 2 / 100

⇒      z = ±√2 / 10

it is the product of 1/10 and √2 which is not a rational so

z² = 0.02  is irrational number.

3)     u² = 17 / 4

⇒      z = ±√17 / 2

it is the product of 1/2 and √17 which is not a rational so

z² = 17/4  is irrational number.

4)     w² = 27

⇒      z = ±3√3

it is the product of 3 and √3 which is not a rational so

w² = 27  is irrational number.

5)     t^4 = 256

⇒      z = ±4 = ±4 / 1

Which can written in p/q form where p and q ∈ Integers and q ≠ 0

SO   t^4 = 256 is rational number.

hope it helps