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

Which of the following results in a sum or a product that is rational? Choose all-example-1
User An Hoa
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1 Answer

3 votes

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.

User Doruk
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