Question

Ok here is another Simplify question I do need it broken down cause its not making sense.

Cube square root of -27

Answer 1

your question is \[\Large \sqrt[3]{-27}\] right?

here's a hint
\[1^3 = 1\]
\[2^3 = 8\]
\[3^3 =27\]
\[4^3 = 64\]
\[5^3 = 125\]
etc.
does that help?

Answer 2

she is asking about the negative part i think it will be following what is called principal root so all answers is positive right???

So its 3 I guess

Answer 3

3i (i=iota)

Answer 4

iota??? what does that mean

Answer 5

\[\sqrt[3]-27 =\sqrt[3]{-9 } x 3 = \]

Answer 6

@mandypruitt you're pretty close..
\[\LARGE \sqrt[3]{-27} \implies \sqrt[3]{-3 \times -3 \times -3} \implies \sqrt[3]{(-3)^3}\]
can you see it now?

Answer 7

\[\sqrt[3]{-9} . \sqrt[3]{3}\]

Answer 8

hint: \[\huge \sqrt[m]{(a)^m} \implies a\]

Answer 9

try to recall the rules about the sign when multiplying and dividing negative and positive integers xD

Answer 10

I forsome reason cant get passed \[\sqrt[3]{-9} \times \sqrt[3]{3}\]

Answer 11

@mandypruitt do what i wrote above

Answer 12

i assure you that where you are right now is a dead end

Answer 13

Im sorry but I am at a loss

Answer 14

okay..let's start from the beginning..

Answer 15

do you agree that 27 = 9 x 3?

Answer 16

yes

Answer 17

what about 27 = 3 x 3 x 3

do you agree that is right?

Answer 18

yes

Answer 19

U can write it as \[\LARGE{\sqrt[3]{-1 \times 27}}\]\[\LARGE{\sqrt[3]{-1} \times \sqrt[3]{27}}\]\[\LARGE{3i}\]

Answer 20

so -27 = -3 x -3 x -3

right? -3 x - 3 is +9 then 9 x - 3 is -27

following so far?

Answer 21

yes

Answer 22

now \(\LARGE{3i=3 \times -1=-3 Ans.}\)

Answer 23

-3 * -3 * -3 = ???

Answer 24

so \[\Large \sqrt[3]{-27} = \sqrt[3]{-3 \times -3 \times -3}\]
right?

Answer 25

or simply do it as \[-3 \times -3 \times -3\]

Answer 26

take common of them

Answer 27

-3 ans

Answer 28

yes

Answer 29

so now.. according to algebra \[-3 \times -3 \times - 3 = (-3)^3\]
right?

Answer 30

yes

Answer 31

no the answer is 3i^2

Answer 32

i^2 =-1 where i=iota

Answer 33

-3*-3*-3 =-27 (-)(-)(-) = (+)(-) = (-)

Answer 34

so \[\Large \sqrt[3]{-3 \times -3 \times -3} \implies \sqrt[3]{(-3)^3}\]
you're still following right?

Answer 35

ok cuberoot of -27 = -3 xD

Answer 36

yes

Answer 37

I am right the answer is 3i^2

Answer 38

good.. now refer to the algebra rule i posted a while ago \[\huge \sqrt[m]{a^m} \implies a\]
so what do you think is the value of \[\huge \sqrt[3]{(-3)^3}\]

Answer 39

-3 ONLY

Answer 40

It Becomes Complex guys

Answer 41

\[\LARGE\sqrt{(-3)^3}{}\]\[\LARGE{(-3)^{3\times 1\over 3}}\]

Answer 42

-3

Answer 43

no ^ 3i^2 is the answer i can challenge u guys

Answer 44

maybe you guys should debate somewhere else?

Answer 45

My answer is correct dude

Answer 46

no its not and leave convo

Answer 47

hey guys -3 is the answer \(\LARGE100 percent\)

Answer 48

Have you guys studied complex numbers

Answer 49

yes!

Answer 50

please debate somewhere else =_= it's making the post laggy

Answer 51

And You dont know what to answer when u see see a negative sign in underroot

Answer 52

you guys are just confusing me more so I guess I will figure it out somewhere else.

Answer 53

I am out sorry for worrying you @mandypruitt

Answer 54

we should write it as \(i\)

Answer 55

@hba :)

Answer 56

to tell you frankly...they're debating on the same answer :|

Answer 57

^^ Thats what i am saying

Answer 58

I agree its 3i

Answer 59

\[3i^2 = 3(-1) = -3\]
=_= why the heck are you guys fighting over the same answer

Answer 60

\[\LARGE{\sqrt[3]{-1 \times 27}}\]\[\LARGE{\sqrt[3]{-1} \times \sqrt[3]{27}}\]

Answer 61

anyway @mandypruitt
\[\large \sqrt[3]{-27} \implies \sqrt[3]{-3 \times -3 \times -3} \implies \sqrt[3]{(-3)^3} \implies -3\]
do you get it?

Answer 62

cube root of 27=3
cube root of -1=i

Answer 63

no @jiteshmeghwal9

Answer 64

3i=3*-1=-3

Answer 65

that's ht i wanna say @lgbasallote

Answer 66

cube root of -1 is -1

square root of -1 is i

Answer 67

wht*

Answer 68

oops sorry i don't see tht

Answer 69

right when odd its the same sign but when even there opposite

Answer 70

OK so WHY do you get -3 from the last equation you wrote.

Answer 71

Oh wait it just dawned on me

Answer 72

oh lol that's good

Answer 73

its perfect square root thats why I was reading into something that was not there

Answer 74

perfect cube root*

Answer 75

oops duh lol

Answer 76

hehe

Answer 77

right you are somehow lucky to have such a large audience xD

Answer 78

lol ^

Answer 79

thanks @hba