Question

I need help with simplifying radicals please?

Answer 1

Do you mean radicals with numbers under them? Variables? Both?

Answer 2

example:
\[\sqrt{4x ^{6}}\]

Answer 3

Well, there's more than one way but here's the way I think is simplest....

take the numbers under the radical and break it down into its prime factors using a factor tree. So in this case, 4=2*2.

Then take the variables and write them out the 'long' way...instead of x^6, write x*x*x*x*x*x

Then since it is a square root, go through your list of factors (the two's and the x's) and circle groups of two alike factors. Every factor that is in a group of two gets to come outside the radical.

I'm bad at using the equation editor, but I'll try....

Answer 4

\[\sqrt{4x ^{6}}\]

\[\sqrt{2*2*x*x*x*x*x*x}\]

\[\sqrt{(2*2)(x*x)(x*x)(x*x)}\]

=2*x*x*x

or \[2x ^{3}\]

Answer 5

If you were trying to simplify a cube-root, you'd made groups of 3 like factors instead of groups of twos.

Answer 6

but the answer is \[2\left| x ^{3} \right|\]

Answer 7

Yeah - because you don't know if x is positive or negative, you should use the abs. value when you are taking an even root, but most textbooks quickly move beyond that. Sorry - forgot about that!

Answer 8

Lol, it's okay. But I don't understand when to put abs. value and where?

Answer 9

whenever you have an even root (so a square root, a 4th root, a 6th root, etc) and you take some variables OUT of the radical, you use the abs. value. You don't need it for the numbers that come out or if you have an odd root (a cube root, a 5th root, etc)

Answer 10

OH! Thank you so much! :D

Answer 11

waiit, I'm so sorry to bother you but. . .

Answer 12

\[\sqrt[4]{x ^{4}y ^{8}}\]

the answer is \[\left| x \right|y ^{2}\]

Answer 13

Sorry I didn't answer this yesterday...I guess because y^2 is always positive, you don't have to do the abs. values. It's a picky thing.

Answer 14

oh okay, thanks