Question

simplify each radical expression: radical 144x^3y^4z^5

Answer 1

what is the square root of 144 ?

Answer 2

we need to get that out of the way first
this one is a bit harder than the last one, but only a bit harder, not much

Answer 3

its 12

Answer 4

ok good, so we know 12 comes outside of the radical
now how many times does 2 go in to 3 ?

Answer 5

just once

Answer 6

yes, just once, but it leaves a remainder of 1, (unlike the last example) so
\[\sqrt{x^3}=x^1\sqrt{x^1}=x\sqrt{x}\]

Answer 7

we do the same for \(\sqrt{y^5}\)
how many times does 2 go in to 5 ?

Answer 8

2 times and a remainder of 1

Answer 9

zactly
so \[\sqrt{z^5}=z^2\sqrt{z}\]

Answer 10

well it should be a \(y\) but you get the idea

Answer 11

final answer is therefore
\[12xy^2\sqrt{xy}\]

Answer 12

ohh okay thank you so much i appreciate it

Answer 13

yw