Question

hey i need a lot of help i do not understand this class at all and i am on the verge of failing pleas help.

A student is attempting to show that the product of a nonzero rational number and an irrational number is always rational or always irrational.

Part A: Find the value of zero point 17 repeating times square root of 108 end square root and place it in simplified form.

Part B: Is the answer in Part A irrational or rational? Make a conjecture about the product of a nonzero rational number and an irrational number.

Answer 1

@imqwerty i dont know this.....could you possibly help?

Answer 2

sure
i can help :)

Answer 3

yay thank you

Answer 4

ok so did you try to solve this :)
are you stuck somewhere?

Answer 5

to be honest i dont understand the question to much. This class is way to advanced for me

Answer 6

ok 1st lets look at \(Part~A\)

it says that we need to find the value of-> \(0.17171717... \times \sqrt{108}\)
right?

Answer 7

yes

Answer 8

are you allowed to use calculators?

Answer 9

yea this is a flvs class

Answer 10

ok then just use a calculator to solve the \(\cal\color{Black}{Part~A}\)

Answer 11

tell me what you got as the answer :)

Answer 12

i got 18.54545436

Answer 13

its wrong
I think you didn't enter the values correctly in the calculator
please recheck :)

Answer 14

i got a really long number 1.7845

Answer 15

yes now its correct \(\huge\ddot\smile\)
Do you know what are the properties of irrational numbers?

Answer 16

kinda

Answer 17

Ok i'll tell you

\(\cal\huge\color{Violet}{Properties~Of~Irrational~Numbers}\)

\(\cal\large\color{black}{Property~1->}\)Irrational numbers cannot be represented in this form->\(\frac{ p }{ q }\) here \(\color{red}{p}\) and \(\color{red}{q}\) are coprime numbers.

\(\cal\large\color{black}{Property~2->}\)Irrational number are non terminating and non- repeating.
For example->1.78453717783..

here we can see that this is a really long number :)
and notice that the numbers after the decimal place do not repeat in a definite pattern like they do in this number->\(0.171717\)

Answer 18

so that would make the answer an irrational number

Answer 19

yes the answer is irrational because it follows the given rules :)

but now the \(Part~B\) also wants us to prove that the product of a nonzero rational number and an irrational number.

and now we gonna prove this thing
ok?

Answer 20

ok

Answer 21

so we know that \(0.1717171717... \times \sqrt{108}=1.7845..\) is irrational

similarly when you calculate the value of \(\sqrt{108}\) using calculator it comes to be irrational.

what can you say about 0.171717 is it following all the rules to be irrational?

Answer 22

no it is not following all the rules it is repeating

Answer 23

yes so it is rational and not irrational :)

it is also a property of rational numbers to follow repetition in a certain pattern :)

so 0.17171717.. is rational

\(\sqrt{108}\) is irrational

and then we multiply them what do we get?
rational or irrational? :)

Answer 24

irrational

Answer 25

yes :)

so can we say that
\(Rational \times Irrational= Irrational\) ?

Answer 26

yes

Answer 27

yes correct :)
i think we have finished this ques

Answer 28

thank you so much

Answer 29

no problem :)