Question

Simplify

Answer 1

\[\frac{ \sqrt[4]{400} }{ \sqrt[4]{5}}\]

Answer 2

Please explain/show your work so i understand

Answer 3

@dan815

Answer 4

@Michele_Laino

Answer 5

hint:
we can write:
\[\Large \frac{{\sqrt[4]{{400}}}}{{\sqrt[4]{5}}} = \sqrt[4]{{\frac{{400}}{5}}} = \sqrt[4]{{\frac{{25 \times 16}}{5}}} = ...\]
please continue

Answer 6

I dont know how to square this, I'm totally lost lol that's why i need the help and for someone to explain how we get to the answer

Answer 7

what is:
25/5=...?

Answer 8

5

Answer 9

ok! so we can write this:
\[\frac{{\sqrt[4]{{400}}}}{{\sqrt[4]{5}}} = \sqrt[4]{{\frac{{400}}{5}}} = \sqrt[4]{{\frac{{25 \times 16}}{5}}} = \sqrt[4]{{5 \times 16}}\]

Answer 10

\[\large \frac{{\sqrt[4]{{400}}}}{{\sqrt[4]{5}}} = \sqrt[4]{{\frac{{400}}{5}}} = \sqrt[4]{{\frac{{25 \times 16}}{5}}} = \sqrt[4]{{5 \times 16}}\]

Answer 11

next, please keep in mind that:
\[\Large 16 = {2^4}\]

Answer 12

ok so what do we do with the 16 than?

Answer 13

here is the next step:
\[\Large \sqrt[4]{{5 \times 16}} = \sqrt[4]{5} \times \sqrt[4]{{16}} = \sqrt[4]{5} \times \sqrt[4]{{{2^4}}}\]

Answer 14

Where did the 25 come from? like when you splits it to 25x16 how did you get those numbers?

Answer 15

since:
\[\Large 400 = 25 \times 16\]

Answer 16

Ok i see now

Answer 17

step by step:
\[\large 400 = 4 \times 100 = 4 \times \left( {4 \times 25} \right) = \left( {4 \times 4} \right) \times 25 = 16 \times 25\]

Answer 18

now, do you know how to simplify:
\[\Large \sqrt[4]{{{2^4}}}\]?

Answer 19

Sorry im catching up my computer froze

Answer 20

\[2\sqrt[4]{5}\]

Answer 21

that's right, since:
\[\Large \sqrt[4]{{{2^4}}} = {2^{4/4}} = {2^1} = 2\]

Answer 22

or you can use windows calculator, to compute this:
\[\Large \sqrt[4]{{{2^4}}} = \sqrt[4]{{16}} = 2\]

Answer 23

Sweet, thank you very ,much for guiding me along instead of giving me the answer, i like to understand how to get to the answer

Answer 24

:)