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Mathematics 42 Online
OpenStudy (anonymous):

Explain why rational exponents are not defined when the denominator of the exponent in lowest terms is even and the base is negative

OpenStudy (zzr0ck3r):

assume x > 0 then (-x)^(1/2) = sqrt(-x) and we cant take sqaure roots of negative nnumbers.............yet

OpenStudy (zzr0ck3r):

so (-3)^(1/4) is \[\sqrt[4]{-3}\] which is not ok but \[\sqrt[3]{-3}\] is fine

OpenStudy (anonymous):

such square roots are possible in complex number system.....if u'll probably not know about it if u r learning elementary number theory......but as for real number system such square root s are not possible..

OpenStudy (zzr0ck3r):

make sense?

OpenStudy (anonymous):

still confused sorry

OpenStudy (zzr0ck3r):

what is the square root of -2?

OpenStudy (anonymous):

doesnt exist

OpenStudy (zzr0ck3r):

what is the 3rd root of -8?

OpenStudy (anonymous):

2

OpenStudy (zzr0ck3r):

-2 right?

OpenStudy (anonymous):

-2

OpenStudy (zzr0ck3r):

so you cant take the squared but you can take the qubed root of a negative number right?

OpenStudy (anonymous):

right

OpenStudy (zzr0ck3r):

in other words (-1)^(1/2) does not have an answer but (-1)^(1/3) does

OpenStudy (anonymous):

yes

OpenStudy (zzr0ck3r):

extend that and (-1)^(1/(even number)) has no answer but (-1)^(1/(odd number)) does

OpenStudy (zzr0ck3r):

when I say extend that I just mean extend the idea

OpenStudy (zzr0ck3r):

(-1)^(1/2) = not ok (-1)^(1/3) = ok (-1)^(1/4) = not ok (-1)^(1/5) = ok (-1)^(1/6) = not ok (-1)^(1/7) = ok

OpenStudy (anonymous):

ok how could you explain this in words?

OpenStudy (zzr0ck3r):

we cant take the nth root of a number unless n is odd

OpenStudy (zzr0ck3r):

err we cant take the nth root of a negative number unless n is odd

OpenStudy (anonymous):

because why?

OpenStudy (zzr0ck3r):

because nth roots of a negative number when n is even are undefined such as sqrt(-2)

OpenStudy (zzr0ck3r):

because nothing times itself is negative

OpenStudy (zzr0ck3r):

a*a is always positive when a is a real number

OpenStudy (anonymous):

and thats the explanation?

OpenStudy (zzr0ck3r):

we cant take the nth root of a negative number unless n is odd because nth roots of a negative number when n is even are undefined such as sqrt(-2)

OpenStudy (zzr0ck3r):

understand it and say it however you want.

OpenStudy (zzr0ck3r):

your teacher is not looking for a proof, just wants you to understand the language and the know how.

OpenStudy (anonymous):

ok this was very helpful thank you!

OpenStudy (zzr0ck3r):

x^(1/2) the 1/2 part is the rational exponent so the denominator is the number we are concerned with.

OpenStudy (zzr0ck3r):

aight man i got to sleep goodluck

OpenStudy (anonymous):

thank you!!!!

OpenStudy (zzr0ck3r):

for sure

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