Answer:
(a) Three numbers that could be Jenny's favorite number are;
2, 8, and 18
(b) Yes
Step-by-step explanation:
(a) Let Jenny's favorite integer be X, we have;
√X × √2 = Y where Y is an integer
Therefore, the square root of Jenny's favorite number has a factor of √2 which gives the possible options as
2 with √2 being the square root
8 with √8 = 2·√2
18 with √18 being 3·√2
(b) By dividing each of the square root of the possible Jenny's favorite number, we have;
i) For the integer 2 we have;
√2/√2 = 1 which is an integer
ii) For the integer 8 we have;
√8/√2 = 2·√2/√2 = 2 which is an integer
ii) For the integer 18 we have;
√18/√2 = 3·√2/√2 = 3 which is an integer
