Question

Medal to most helpful. Simplify 2 times the 4th root of 80. Thanks.

Answer 1

\[2 \sqrt[4]{80}\]

Answer 2

\(\large\color{#000000 }{ \displaystyle 2\cdot \sqrt[4]{80} }\)

Answer 3

\(\large\color{#000000 }{ \displaystyle 2\cdot \sqrt[4]{80} }\)

\(\large\color{#000000 }{ \displaystyle 2\cdot \sqrt[4]{16\times5} }\)

\(\large\color{#000000 }{ \displaystyle 2\cdot \sqrt[4]{16}\times\sqrt[4]{5} }\)

Answer 4

Can you go from there?

Answer 5

Could you continue from there, please? @SolomonZelman

Answer 6

Do you know what "forth root" means?

Answer 7

one fourth power

Answer 8

2 * 16^1/4 * 5^1/4 ??

Answer 9

But that second component is integer when simplified.

Answer 10

I will try to make the definition clear through one example.
Just stay with me please

Answer 11

You know that,
\(\large\color{#000000 }{ \displaystyle 3\times 3\times 3\times 3 =81 }\)

Ok?

Answer 12

okay

Answer 13

Ok, good, and how many times did I multiply the 3?

Answer 14

4 times

Answer 15

Yes

Answer 16

\(\large\color{#000000 }{ \displaystyle \underbrace{3\times 3\times 3\times 3 }_{4~\rm times}=81 }\)

Answer 17

I'm following.

Answer 18

And that would mean

\(\large\color{#000000 }{ \displaystyle 3^4=81 }\)

Answer 19

And the inverse operation of \(\large\color{#000000 }{ \displaystyle 3^4=81 }\),
is,

\(\Large\color{#000000 }{ \displaystyle \sqrt[\color{red}{4}]{81} =3}\)

Answer 20

\(\large\color{#000000 }{ \displaystyle \sqrt[4]{81}=3 }\) and/because \(\large\color{#000000 }{ \displaystyle 3^4=81 }\)


So, this way,

\(\large\color{#000000 }{ \displaystyle \sqrt[4]{16}={\bf \quad is~?} }\)

Answer 21

(try dividing 16 by 2 a bunch of times and tell me that 2^what? = 16)

Answer 22

Answer Choices: (Just for reference)

A. \[4\sqrt[4]{5}\]
B. \[8\sqrt[4]{5}\]
C. \[16\sqrt[4]{5}\]
D. \[32\sqrt[4]{5}\]

Answer 23

(This way you would be able to determine the 4th root of 16)

Answer 24

2?

Answer 25

Explain your question

Answer 26

sorry it took so long i had to refresh openstudy

Answer 27

the answer to your question is 2. the fourth root of 16

Answer 28

Yes,

the 4th root of 16 is 2.

Answer 29

So let's come back to our problem.

Answer 30

okay

Answer 31

\(\large\color{#000000 }{ \displaystyle 2\cdot \sqrt[4]{80} }\)

\(\large\color{#000000 }{ \displaystyle 2\cdot \sqrt[4]{16\times5} }\)

\(\large\color{#000000 }{ \displaystyle 2\cdot \sqrt[4]{16}\times\sqrt[4]{5} }\)

this is where we left.

Answer 32

yep

Answer 33

\(\large\color{#000000 }{ \displaystyle 2\cdot \color{red}{2}\times\sqrt[4]{5} }\)

Answer 34

So your most simplified answer is?

Answer 35

(Note that there is NO way to simplify \(\large\color{#000000 }{ \sqrt[4]{5} }\))

Answer 36

\[4\sqrt[4]{5}\]

Answer 37

Yup, that's exactly right!

Answer 38

Okay, thank you for your help! I appreciate it. Cheers!

Answer 39

YW