Step by step
The question
Question: is √64 rational or irrational?
√64
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.
7 times 7 is 49.
8 times 8 is 64.
9 times 9 is 81.
Squares: 7² = 49, 8² = 64, 9² = 81
64 is a square number: 8 times 8.
So √64 is 8, a whole number.
8 is 8/1.
= √64 = 8 = 81
Careful!
A root sign does not always mean irrational.
√64 is just 8.
Careful: a √ sign does not make it irrational
So √64 is rational.
It is a whole number.
= √64 is rational
2 Check
Let's check: 8 times 8 is 64.
So √64 really is 8.
So the answer is right!
8 × 8 = 64
Let's look back.
First: look for a square number.
Last: check.
Answer
= √64 is rational