Step by step
The question
Question: is √144 rational or irrational?
√144
Rational means: it can be written as a fraction, with whole numbers on top and at the bottom.
Then its decimal stops, or repeats for ever.
Irrational means: no fraction works.
Its decimal never stops and never repeats.
rational = a fraction of whole numbers
decimal stops or repeats
1 Look for a square number
Square numbers are a number times itself.
11 times 11 is 121.
12 times 12 is 144.
13 times 13 is 169.
Squares: 11² = 121, 12² = 144, 13² = 169
144 is a square number: 12 times 12.
So √144 is 12, a whole number.
12 is 12/1.
= √144 = 12 = 121
Careful!
A root sign does not always mean irrational.
√144 is just 12.
Careful: a √ sign does not make it irrational
So √144 is rational.
It is a whole number.
= √144 is rational
2 Check
Let's check: 12 times 12 is 144.
So √144 really is 12.
So the answer is right!
12 × 12 = 144
Let's look back.
First: look for a square number.
Last: check.
Answer
= √144 is rational