Question

Which of the following results in a sum or a product that is rational? Choose all that apply. (3 points)

Answer 1

Remark

It is easier in this case to state the irrational ones and then talk about the rationals.

sqrt(2) * sqrt(3) is irrational. The square root of 6 fills your calculator's window with many numbers and there is no pattern to them. Sqrt(6) cannot be expressed as a fraction or a repeating decimal which is also a fraction.

The last one is also irrational for the same reason. 3*pi cannot be expressed as either a repeating decimal or a fraction.

All the others are rational. The one you might have trouble with is the first one.

0.12 repeating is actually found by letting x = 0.12121212121212121212...Then

100 x =  12.121212121212121212 ...

      x =    0.121212121212121212...     Subtract

99 x = 12

x = 12/99

So the mixed fraction you get is 3 12/99 which is 309/99

When you multiply that by 1.4 it does not change the fact that you still get a fraction. It turns out to be 721 / 165.  The method is similar to the one used to get 12 / 99. I don't think you need to know the exact answer. You need only need to know that the first one is rational.

Choice 2 is rational because 9 and 25 are  perfect squares. sqrt(9) = 3

Sqrt(25) = 5.

3*5 = 15.

Answer

One Two are four are all rational.