## anonymous one year ago Simplify

1. anonymous

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

2. anonymous

3. anonymous

@dan815

4. anonymous

@Michele_Laino

5. Michele_Laino

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

6. anonymous

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

7. Michele_Laino

what is: 25/5=...?

8. anonymous

5

9. Michele_Laino

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

10. Michele_Laino

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

11. Michele_Laino

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

12. anonymous

ok so what do we do with the 16 than?

13. Michele_Laino

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

14. anonymous

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

15. Michele_Laino

since: $\Large 400 = 25 \times 16$

16. anonymous

Ok i see now

17. Michele_Laino

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

18. Michele_Laino

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

19. anonymous

Sorry im catching up my computer froze

20. anonymous

$2\sqrt[4]{5}$

21. Michele_Laino

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

22. Michele_Laino

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

23. anonymous

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

24. Michele_Laino

:)