Question

Need help please! Select "Rational" or "Irrational" to classify each number.

Rational Irrational
45
4√5
π
25√4

Answer 1

45 = Rational

4√5 = Irrational = 8.9...

π = Irrational = 3.14...

25√4 = Rational = 50

Answer 2

45, Rational. 4√5, Irrational. π

, Irrational 25√4, Rational.

Explanation:

1) A number is rational if it can be written as
`(p)/(q)`

`(45)/(1)=45` So, 45 is a rational one.

2) 4√5, Irrational.

`Assuming \: √(5)\: is\: rational\:number\: then:\\(p)/(q)=√(5)\\\left ( (p)/(q) \right ) ^(2)=(√(5))^(2)\\ (p^(2))/(q^(2))=5\Rightarrow 5p^(2)=q^(2)`

5 divides p and is a common factor of q. So this is a contradiction.
`(p)/(q)`. So √5 cannot be rational, then it is a Irrational. And a not terminating number multiplied by any factor is still an irrational number.

3) π, Irrational.

Similarly this number could be undergone to the same proof. This is an Irrational number. Not terminating.

4) 25√4, Rational

`25√(4)=25*2=50\Rightarrow (50)/(1)=(100)/(2)=(200)/(4)`