Question

Assume a and b are nonzero rational numbers and c and d are irrational numbers. For each of the following expressions, determine whether the result is irrational, rational, or both. Justify your answers.

Part A: ac + d

Part B: four b square root of three end square root plus c

Part C: b2(c + d)

Answer 1

Well product of two rationals is always rational. And the sum of a rational and an irrational is irrational.

Answer 2

That's for part A.

Answer 3

They give you too much freedom in your choice though.
Like for part A, what if we let
b=-1 (rational)
c=pi (irrational
d=pi (irrational)

Then bc+d = -pi + pi = 0 (rational)

Maybe they didn't want you to consider 0
because otherwise all of these options can be rational.
Hmmm

Answer 4

Woops I meant a=-1
sorry :D

Answer 5

You chose two irrationals, you're only asked to choose 1 in part A.
Part is always gonna give you an irrational.

Answer 6

Part A*

Answer 7

Here's what you need to remember in general :
x
product of two rationals is always rational
product of two irrationals can be both
product of a non-zero rational and an irrational is irrational
+
sum of two rationals is always rational
sum of two irrationals can be both
sum of a rational and an irrational is always irrational

Answer 8

I am completely lost... :(

Answer 9

@zepdrix

Answer 10

What part do you still have problems on ?

Answer 11

Btw I misread part A, it's product of a non-zero rational (a) and an irrational (c) which is irrational. Then the sum of 2 irrationals (ac) and (d) which can be both. So part A can be both rational and irrational.

Answer 12

I dont understand that lol if i were to have the written answer i would be able to work from it, i dont want to sound like a dummy that just wants the answer but its hard to understand something i do not know without knowing the correct answer, i can work from the answer and understand the plug it all in.

Answer 13

:d

Answer 14

what lol

Answer 15

what's going on? :o
confusing math?

Answer 16

Do you understand the difference between a rational and irrational number?
Rationals can be written as a fraction containing whole numbers.
Irrationals can not.

Here are some examples of rational numbers:
\(\rm \frac32\) is rational because its a whole number divided by a whole number.
\(\rm 7\) is a rational number because it can be written as \(\rm \frac71\).
\(\rm -4\) is a rational number, it also can be written in this form \(\rm \frac{-4}{1}\).

This next one maybe seem surprising, but,
\(\rm 0\) is a rational number. It also can be written as \(\rm \frac01\),
but not as \(\rm \frac00\) (Which is not a number).

Answer 17

Oh here are some examples of irrational numbers:
`The square root of any number that is NOT a perfect square.`
So \(\rm \sqrt3\) is irrational.
There is no fractional representation of square root 3 using whole numbers.
Same for \(\rm \sqrt5\), \(\rm \sqrt6\), ... all of the numbers which are not 4, 9, 16, etc.

Answer 18

So if you have something like \(\rm 4+\sqrt3\),
this is an example of a `rational number` plus `an irrational number`.
The result is irrational because it has the irrational part in it.
\(\rm 4+\sqrt3=irrational\)

Answer 19

Ok I should stop rambling probably D:
I dunno where you're stuck.

Answer 20

Go eat a sandwich, sandwiches are good for you.