# New concept: cube roots, 4th root, etc

#1

I found out how to do cube roots, using fractional powers. I found it out when in math class we were getting off topic and someone wanted to know how to do 32^.6, and it gave me the idea when I found out to do it you do (5√32)^2, so I was able to make this:

This concept is FTU if you give credit

• no
• yes

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#3

#4

I haven’t looked at the project yet, but there’s a problem with the lead in.

32^.6 doesn’t = (5√32)^2

It’s probably just a typo but so others aren’t mislead (and to show why)

X^(1/n) = n√X
and
(X^n)^m = X^(n*m)

So
X^(m/n) = (n√X)^m

therefore
32^.6 = 32^(6/10) = 32^(3/5) = (5√32)^3

By the way, I think it’s awesome that you’ve made a Hopscotch project out of something interesting you learned in math class!

#5

It means to the 5th root, I just didn’t know how to raise the number

#6

No worries. It’s just that without being told, one can’t know what the root is without also knowing what the exponent is.

If it was 32^.75 this wouldn’t be something to the 5th root, right? It’d be (4√32)^3 Just remember to turn the decimal into a fraction, simplify it, and the denominator (bottom part) is the root, while the numerator (top part) is the exponent.
.75 = 3/4 (which is already simplified), so it’s 32 to 4th root cubed (^3)

#7

I think I’m doing this right:

32 ^ (.6) = 34 ^ (6/10)

= (34 to the 10th root)^6

(There’s no way to show it in the index)

#8

Yes, technically that’s right. But 6/10 isn’t simplified so a math teacher may deduct points and in general we should always simplify.

32^.6 = 32^(6/10) = 32^(3/5) = (5√32)^3

#9

I am a little late replying, but this is a really good idea and a good project. Great job!

#11

Yeah, cool, Xse. You don’t fool us

#12

You can use fraction s to find roots. (2^0.5= sqrt(2))