Question

What is the simplified form of the expression 4the square root of v. + 4 the square root of v to the sixth power. − the square root of the quantity 25 times v. − the square root of the quantity 9 times v to the sixth power.?

Answer 1

i dont know where to start..

Answer 2

\[4\sqrt{v}+4\sqrt{v^6}-\sqrt{25v}-\sqrt{9v^6}\]??

Answer 3

like that? hard to read

Answer 4

yes exactly that

Answer 5

ok fine
lets take it step by step

Answer 6

\[\sqrt{v^6}\] is the square root of \(v^6\)
since \(2\) goes in to 6 3 times, this is the same as \(v^3\)

Answer 7

another way to see it is
\[\sqrt{v^6}=\sqrt{(v^3)^2}=v^3\]

Answer 8

now \(\sqrt{25v}=\sqrt{25}\times \sqrt{v}=5\sqrt{v}\)

Answer 9

and finally since we already know \(\sqrt{v^6}=v^3\) we know
\[\sqrt{9v^6}=3v^3\]

Answer 10

now we have
\[4\sqrt{v}+4v^3-5\sqrt{v}-3v^3\] and all that is left is to combine like terms

Answer 11

\(4v^3-3v^3=v^3\) and \(4\sqrt{v}-5\sqrt{v}=-\sqrt{v}\) for a "final answer" of
\[v^3-\sqrt{v}\]

Answer 12

wow thats alot of steps, thank you so much, im going to go over and rad this a few times to fully unnderstand it, but hanks again so much!

Answer 13

it is a lot of steps
but that is largely because i was explaining as i went along, and skipped nothing
with some practice you can do most of this in your head

Answer 14

no steps were skipped, so if you really do read it, you will see all that you need to use to solve it

Answer 15

oh, and your welcome!

Answer 16

This man ( @satellite73 ) deserves a cookie :D lol