Question

Which of the following statements is false?

Answer 1

A. The sum of two rational numbers is always rational.
B. The product of a nonzero rational number and an irrational number is always irrational.
C. The product of two rational numbers is always rational.
D. The sum of two irrational numbers is always rational.

Answer 2

@hartnn @3mar ?

Answer 3

please describe how to get the answer too

Answer 4

@Directrix ?

Answer 5

@zepdrix ?

Answer 6

Let's look at option A first.
`The sum of two rational numbers is always rational.`\[\large\rm \frac23+\frac59\]

Remember a rational is a number that can be written in the form: \(\dfrac a b\) where a and b are integers.

So that's what I did, I constructed two rational numbers.
Will they always give you a rational number when you add them together?
Will they always give you another fraction?

Answer 7

plz help me, ive been on this 4 QUESTION TEST FOR THE PAST 2 HOURS!!

Answer 8

and no, no to the question above

Answer 9

? 0_o

Answer 10

no to your question

Answer 11

Why would adding fractions not give you a fraction?

Answer 12

it wouldn't ALWAYS, but most of the time

Answer 13

\[\large\rm \frac{2}{3}+\frac{4}{3}=\frac{6}{3}\]It would `all of the time`.
Even in this example, we end up with 6/3 (which is a fraction).
Sure, you can write it as 2 in a more simplified way.
But it can always be written as a fraction, yes? :o

Answer 14

yes.. ok!

Answer 15

Nice presentation, zepdrix

Answer 16

How bout rational x irrational?
Maybe we'll take 2 as our rational number,
and pi as our irrational,
\(\large\rm 2\times\pi=2\pi\)

Answer 17

Or even \(\large\rm 5\times\pi\)
This is just a group of irrationals, ya?
A bunch of pi's.
So it's still irrational.

Answer 18

and 2pi is... irrational?

Answer 19

ok yup

Answer 20

How about option D? Let's think about that one.
Let's choose two irrational numbers...
Remember that when you take the square root of a number,
only the perfect squares are rationals.

\(\large\rm \sqrt{4}=2\qquad\qquad \sqrt{9}=3\qquad\qquad \sqrt{16}=4\)

So if we take the square root of any value between 4 and 9, it will be irrational.
Let's multiply a couple together and see what happens,
\(\large\rm \sqrt{5}\times\sqrt{7}=?\)

Answer 21

Oh it said sum! My bad

Answer 22

Since we're dealing with a sum, it's probably easier to use the pi example again,\[\large\rm \pi+\pi\]

Answer 23

either way, its still irrational

Answer 24

Good!
So I guess option D is the liar :)

Answer 25

so that only leaves C!

Answer 26

No no.
Option D is the `false` one.

Answer 27

ohhh... lol I forgot the question XD thanks so much!

Answer 28

D. The sum of two irrational numbers is always `rational`.

We did our own detective work and found out that it's always `irrational`.

Answer 29

:3

Answer 30

thanks so much :)