Question

Which of the following results in a sum or a product that is rational? Choose all that apply

A.4+9
B.PI*5
C.3.45*1.2
D.sqrd16*sqrd4
E.sqrd7*sqrd2

sqrd=square root. the 3.45 has a line over the 45 I didn't know how to do that on here.

Answer 1

any number with pi in it is not rational.
any number with sqrt 7 in it or sqrt 2 in it is not rational

all the others can be expressed as a ratio of whole numbers.

13/1

3.454545454545.....
= 3 + 45/100 + 45/10,000 + 45/ 1,000,000 etc
= 3 + 45/100 + 1/100 (45/100)+ 1/100^2 (45/100)
geometric series a=45/100, r = 1/100
see http://www.mathsisfun.com/algebra/sequences-sums-geometric.html

sum = a (1/(1-r)) = 45/100(1/.99)
= 45/99
so
3.454545.... = 3 + 45/99 = 342/99


4 * 2 / 1

Answer 2

I can select three choices, which ones are correct?

Answer 3

I told you all but B and E
Make sure you understand C, how to express a repeating decimal as a ratio of whole numbers (rational) using infinite geometric sequence.

Answer 4

ok thanks Damon