Step by step
The question
Question: is √81 rational or irrational?
√81
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.
8 times 8 is 64.
9 times 9 is 81.
10 times 10 is 100.
Squares: 8² = 64, 9² = 81, 10² = 100
81 is a square number: 9 times 9.
So √81 is 9, a whole number.
9 is 9/1.
= √81 = 9 = 91
Careful!
A root sign does not always mean irrational.
√81 is just 9.
Careful: a √ sign does not make it irrational
So √81 is rational.
It is a whole number.
= √81 is rational
2 Check
Let's check: 9 times 9 is 81.
So √81 really is 9.
So the answer is right!
9 × 9 = 81
Let's look back.
First: look for a square number.
Last: check.
Answer
= √81 is rational