I dont understand this. Also what is the set of numbers square root of 64
what sets of numbers does square root 17 belong to?
When you take the square root of a number, there are two types of answers you might get: A nice number (a whole number or integer) or a not-nice number (a decimal or fraction)*. If you get a nice whole number, then the square root you started with has been simplified. That number is rational**. If you get a not-so-nice number, then the square root you started with is called irrational.
√(17) is irrational, because it's not a "nice" number. √(64) is rational, because it simplifies to 8, a "nice" number.
Math trivia: In Europe, non-nice-number square roots are called "surds". Yup, really!
*It's not really true that decimals and fractions are "not nice" but people do tend to think of them that way. Really, they're just numbers like 7 and 12; they just look different - don't discriminate against them. ;)
**Rational numbers are numbers that can be written as ratios. Ratio is really just a fancy word that means fraction.