1) 2
2) 3
3) 4
4) 3
5) 2
6) 3
7) 1
8) 2
9) 4
10) 4
11) 1
12) √20; because 20 is not a perfect square, so its square root cannot be expressed as a ratio of two integers.
13) √164 is rational because 164 = 4 * 41, and √164 = √(4*41) = 2√41. Wait, that's irrational. Let me recalculate. Actually, none of these are rational. √99 = √(9*11) = 3√11 (irrational), √164 = √(4*41) = 2√41 (irrational), √196 = 14 (rational). So the rational number is √196 because 196 is a perfect square (14²).
14) √2; it is irrational because it cannot be expressed as a ratio of two integers and its decimal representation is non-terminating and non-repeating.
Parent Tip: Review the logic above to help your child master the concept of 8th grade math problems.
