Question

Can someone tell me how to simplify radicals? its on my final today and my teacher didnt even teach it

Answer 1

what kind of radicals

Answer 2

like radical 60x4y2

Answer 3

thats x to the 4th power

Answer 4

\(\sqrt{60x^4y^2}\) note that 60 is \(2^2 * 3 * 5\)\[=\sqrt{2^2 * 3 * 5 * x^4 * y^2}\]\[=2x^2|y|\sqrt{15}\]

Answer 5

wait why is it 2 to the 2nd power?

Answer 6

the general rule is to look for parts of the expression that you can easily take OUT of the square root sign. for example,
\[\sqrt{60}\] = \[\sqrt{4*15}\]
=\[2\sqrt{15}\]

Answer 7

2 to the 2nd power = 4

4*3*5 = 60

Answer 8

oh i see

Answer 9

you have to break it down until you can take things out of the square root sign, like an X^2 can be taken out of the square root sign and turned into an X.

Answer 10

does that make sense aavarino?

Answer 11

yes

Answer 12

so you even do the square root of the exponents

Answer 13

im learning this on my own my teacher didnt even show us how to do these lol

Answer 14

and to simplify should all the variables be outside of the radical?

Answer 15

yup! exactly.

\[\sqrt{x ^{4}}=x ^{2}\]

Answer 16

the goal of simplifying is to get AS MUCH AS YOU CAN out of the radical sign.

Answer 17

\[\sqrt{y ^{2}}=y\]

Answer 18

it's possible that a variable (x or y) may be left inside the radical sign, and that's okay, as long as it's as simple as you can make it.

Answer 19

\[\sqrt{27x ^{4}y}\]

Answer 20

for that one is it \[3x ^{2}y \sqrt{3} ? \]

Answer 21

or did i do it wrong lol

Answer 22

ALMOST, you're very close. the y that is under the radical - you can't reduce that any further. so it stays under the radical along with the 3 you already have under there.

Answer 23

oh!! i gotcha so whatever is already simplified leave in the radical

Answer 24

IF IF IF it was a y^2 under the radical, then you can reduce that to just y, but it isn't in this probelm.

Answer 25

yes, if it's in there to begin with, it must stay in there. it's like a box. you want to take out the stuff you can, and what's left inside is already as simple as it can get. like a 3, or a y.

if you have a 4 left in there though ,then you have to take it out (square root of 4 = 2).

Answer 26

can i give you another one to see if you can do it now?

Answer 27

yes please!

Answer 28

this one is hard, but i think you can do it:

\[\sqrt{40x ^{3}y ^{4}}\]

Answer 29

wait quick question before i do it.. since 40 has a lot of factors can i choose any? would i get the same answer if i chose 10 and 4 or 8 and 5?

Answer 30

great question! sure, just remember that what's left in the radical has to be as simple as possible.

so let's say you break 40 down into: 8 and 5. MAKE SURE YOU NOTICE that 8 can then be further broken down into 4 and 2.

so really, 40 can be broken down into 4 and 2 and 5. OR 40 can be broken down into 4 and 10.

try it both ways, and see if you get the same answer. :-)

Answer 31

\[2y ^{2} \sqrt{4x ^{3}} ?\]

Answer 32

oops i lied

Answer 33

i meant 2 in the radical lol

Answer 34

let's look at just the X^3 under the radical for a second:

\[\sqrt{x ^{3}} = \sqrt{x ^{2}x}\]

how would you reduce that part?

Answer 35

i thought 3 didnt reduce? but the x^2 reduces to x

Answer 36

the second part is right, but X^3 is the same as X*X*X = X^2*X

all those expressions are the same.

Answer 37

ohhhh

Answer 38

so how would the answer look from the question before?

Answer 39

you had some part of it right:

\[2xy ^{2}\sqrt{10x}\]

make sure you can get to that, and if not, ask me for more help please :-)

Answer 40

question.. but cant 10 be simplified?

Answer 41

it can be broken down into 5 and 2, however neither of those is a clean square root so it doesn't make it any simpler. (good question!)

Answer 42

oh ok! for not learning this in class i understand now

Answer 43

well getting the hang of it

Answer 44

great! should we try another one?

Answer 45

i have 2 more on my review sheet. \[\sqrt{100x}/121 \] ( not sure how to do a fraction on here )

Answer 46

\[\sqrt{100x}/121\] like that?

Answer 47

yes

Answer 48

but its all in the radical

Answer 49

oops, that's what i was going for :-)

Answer 50

okay, so can either 100, x, or 121 be reduced?

Answer 51

yes 10, and 11

Answer 52

awesome. but as you noticed the X has to stay inside the radical.

Answer 53

so what would you get?

Answer 54

radical 10x/11 ? does the radical go over the whole fraction?

Answer 55

note that \[\sqrt{100}= 10

the 10 is OUTSIDE the radical. same for the 11.

Answer 56

so the x is the only thing that stays in the radical?

Answer 57

yup!

Answer 58

so you should have