Question

which of the following is equal to \[\sqrt{\sqrt[3]{6}}\]

Answer 1

6 ^1/6

6 ^1/3

6 ^2/3

6 ^3/2

Medal
I will fan if you explain it to me :)

Answer 2

@Austin6i6
Is this one 6 ^1/3 ?

Answer 3

do you know how to write
\[ \sqrt[3]{6} \]
using exponents ?

Answer 4

no, can you teach me?

Answer 5

it's (unfortunately) memorization.

the little 3 in front of the radical sign becomes the denominator (bottom number) in the fraction 1/3
that is the exponent.

Answer 6

I thought so, but I was not quite sure.

Answer 7

the "cube root" or \( \sqrt[3]{6} \) can be written as \( 6^{\frac{1}{3}} \)

Answer 8

So I was right?

Answer 9

that is part of the problem.
so far you have
\[ \sqrt{ \sqrt[3]{6} } = \sqrt{6^\frac{1}{3} }\]

Answer 10

I think I am starting to understand a little more.

Answer 11

a "normal" square root means the "little number" is understood to be 2
in other words
\[ \sqrt{6^\frac{1}{3} }\]
means the same thing as
\[ \sqrt[2]{6^\frac{1}{3} } \]

Answer 12

and the idea is that
\[ \sqrt[2]{stuff} = (stuff)^\frac{1}{2}\]

Answer 13

in other words, wrap up \( 6^\frac{1}{3} \) in parens (think, put it in a package)
then put 1/2 as its exponent

Answer 14

(6^1/3) ^ 1/2

Answer 15

yes. then you remember this rule for exponents
\[ \left( a^b\right)^c = a^{b\cdot c} \]

Answer 16

in this case, multiply the two exponents to get a single new exponent.

Answer 17

do you remember how to multiply fractions ?

Answer 18

top * top
divided by bottom * bottom

Answer 19

1/6 ?

Answer 20

yes. 1/6 is the new exponent
so the answer is
\[ 6^\frac{1}{6} \]

Answer 21

I think I get it now, can I tag you in my later questions to confirm my answer?

Answer 22

I'm signing off. but someone will check your work.

Answer 23

Okay :) thanks for your help!

Answer 24

yw