I know that the answer is 10, but can someone explain why is that so?

[little path]

thanks, I still don't really get it though, could eli5 a bit more?
like why we just neglect 9n + 8n

[wary wyvern]

It's simple, lim as n approaches infinity, 10^n / 10^n = 1 and both 9 and 8 is equal zero so we neglect 9 and 8. Then solve nth root of 10^n = 10.

[sterile kindle]

because for large n, 9^n and 8^n are much smaller than 10^n, so they are negligble and the sum is effectively just the 10^n term

[vague depot]

$\sqrt[n]{10^n+9^n+8^n}=10\sqrt[n]{1+\frac{9^n}{10^n}+\frac{8^n}{10^n}}$

[cobalt tulip]

SWR

[rustic blade]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[shadow nebula]

lmao what

[grave depot]

should be square root 10

[vague depot]

How

[grave depot]

you factored the 10 inside the root

but how is it completly out?

nvm