Roots: rational?
1. √18: irrational — 18 is not a perfect square, so its root never ends and never repeats2. √576: rational — it is exactly 24, and any whole number counts as a fraction over one3. √484: rational — it is exactly 22, and any whole number counts as a fraction over one4. √360: irrational — 360 is not a perfect square, so its root never ends and never repeats5. √28: irrational — 28 is not a perfect square, so its root never ends and never repeats6. √529: rational — it is exactly 23, and any whole number counts as a fraction over one7. √289: rational — it is exactly 17, and any whole number counts as a fraction over one8. ∛729: rational — it is exactly 9, and any whole number counts as a fraction over one9. √223: irrational — 223 is not a perfect square, so its root never ends and never repeats10. √627: irrational — 627 is not a perfect square, so its root never ends and never repeatsFractions, decimals and π
1. 18/7: rational — it is already written as one whole number over another2. 0.626262…: rational — a decimal that repeats forever can still be written as a fraction3. π: irrational — its digits never end and never repeat4. 8: rational — every whole number is a fraction over 15. 0.171717…: rational — a decimal that repeats forever can still be written as a fraction6. 15/5: rational — it is already written as one whole number over another7. √10: irrational — 10 is not a perfect square, so its root never ends and never repeats8. 0.888: rational — a decimal that stops can be written over a power of ten9. 0.59: rational — a decimal that stops can be written over a power of ten10. 30: rational — every whole number is a fraction over 1Between two whole numbers
1. √59 is between 7 and 8: 72. √260 is between 16 and 17: 163. √192 is between 13 and 14: 134. √193 is between 13 and 14: 135. √292 is between 17 and 18: 176. √493 is between 22 and 23: 227. √15 is between 3 and 4: 38. √197 is between 14 and 15: 149. √413 is between 20 and 21: 2010. √139 is between 11 and 12: 11