Question

What is the simplest form of the quotient?

Answer 1

\[^{4\sqrt{400}}\div ^{4\sqrt{5}}\]

Answer 2

What is the square root of 400?

Answer 3

20

Answer 4

So we now have:\[\frac{4\times 20}{4\times \sqrt{5}}\]
Can we eliminate the 4 in numerator and denominator?

Answer 5

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

Answer 6

???

Answer 7

Yes we can eliminate 4 from both numerator and denominator by dividing both by 4 leaving:
\[\frac{20}{\sqrt{5}}\]Now we can multiply numerator and denominator by the square root of 5 to eliminate the radical from the denominator. What does this leave us with?

Answer 8

\[\frac{20}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{20\sqrt{5}}{5}\]
Can you further simplify this so it is no longer a quotient?

Answer 9

\[2\sqrt{5}\]

Answer 10

Not quite. Dividing the numerator by 5 gives:
\[4\sqrt{5}\]

Answer 11

thats not an answer

Answer 12

\[a. 5^{4\sqrt{2}}\]

Answer 13

\[b. 2^{4}\sqrt{5}\]

Answer 14

\[c. 2\sqrt{5}\]

Answer 15

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

Answer 16

last ones D

Answer 17

i thought it was D

Answer 18

Was this the original question?
\[\frac{\sqrt[4]{400}}{\sqrt[4]{5}}\]
If so, it is not what I understood from your question.

Answer 19

idk

Answer 20

@Hero

Answer 21

first comment is part of the question

Answer 22

the four is an index, i think

Answer 23

idk lol

Answer 24

yes its an index

Answer 25

holy crap ive been on this question for an hour

Answer 26

rule on radicals with same indices says \[\frac{ \sqrt[n]{a} }{ \sqrt[n]{b} }=\sqrt[n]{\frac{ a }{ b }}\]

Answer 27

did you see my choices o posted ^

Answer 28

the answer is \[\sqrt[4]{\frac{ 400 }{ 5 }}=\sqrt[4]{80} (D)\]

Answer 29

thank you i thought it was D