Indices question

Why is it that when we normally square root a number the answer must have a +-, e.g. sqrt(9) = +-3, but that when there is a fractional index, the positive root is taken when square rooting, e.g. sqrt(9^3/2) = 3^3 = 27 and not +-3^3 = +-27. Sorry I'm just confused about it- thanks for any help

Reply 1

BobBobson

3

When you square root any number, you always choose the positive answer. eg. sqrt(9) = 3. This is just for the sake of simplicity and so that sqrt can be considered an actual function (functions cant have 2 answers). However, when you have something like x^2 = 9, that simplifies to x = +- sqrt(9), so x = +-3

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Original post by 11owolea

Why is it that when we normally square root a number the answer must have a +-, e.g. sqrt(9) = +-3, but that when there is a fractional index, the positive root is taken when square rooting, e.g. sqrt(9^3/2) = 3^3 = 27 and not +-3^3 = +-27. Sorry I'm just confused about it- thanks for any help

Firstly; the square root of any number is a positive value.

Secondly; as the person said above, you only take into account the

\pm

when square rooting an expression, or variable, depending on it's domain. So if

x

can be any number at all, and it is satisfied by the fact that

x^2=9

, then

x=\pm 3

. If x was restricted to anything less than 0, then our answer is simple -3. Etc...

Lastly; this is only true for even powers. Therefore this result is not true for third, fifth, seventh powers, etc... and any odd power. This is seen from the simple fact that

(-1)^3=-1

because of (-1)*(-1)*(-1) and

(1)^3=1

. Similarly with other odd powers. So a minus number to an odd power is always negtive, while a positive number to an odd power is always positive. With even powers, negative and positive numbers provide positive answers alike. Hence no plus/minus when taking the roots with odd powers.

(edited 7 years ago)

Reply 3

Kevin De Bruyne

21

Original post by 11owolea

Why is it that when we normally square root a number the answer must have a +-, e.g. sqrt(9) = +-3, but that when there is a fractional index, the positive root is taken when square rooting, e.g. sqrt(9^3/2) = 3^3 = 27 and not +-3^3 = +-27. Sorry I'm just confused about it- thanks for any help

This thread may help :h:

Indices question

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