Jenny multiplies the square root of her favorite positive integer by √2. Her product is an integer. a) Name three numbers that could be Jenny's favorite positive integer, and explain why each could possibly be Jenny's favorite integer. b) Suppose Jenny divides the square root of her favorite positive integer by √2. Does she have to get an integer? (Remember, when Jenny multiplies the square root of her favorite integer by √2, she gets an integer.) For part (b), try using each of the numbers you found in part (a) as Jenny's favorite number.

(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