Question

Im trying to understand how to simplify radicals... see comments

Answer 1

\[\sqrt[3]{72x^{5}}y ^{9}\]

Answer 2

2. \[\sqrt{500x ^{8}y ^{5}}\]

Answer 3

exponent rules!\[\huge\rm \sqrt[n]{x^m} = x^\frac{ m }{ n }\]
:P

Answer 4

\[\large 1.~\sqrt[3]{72x^{5}}y ^{9} = (72)^{1/3}\cdot (x^5)^{1/3}\cdot y^9\]\[\large 2.~ \sqrt{500x ^{8}y ^{5}} = (500)^{1/2} \cdot (x^8)^{1/2} \cdot (y^5)^{1/2}\]

Answer 5

why is it 1/2 instead of 1/3 since were taking the 3rd root?

Answer 6

Typo.

Answer 7

ohhh okay.. hold on let me see if I get this..

Answer 8

And leave everything as a whole number, not a decimal.

Answer 9

okay so 72 is 9*8
8^(1/3) is 2. so 2 is on the outside of the radical
9 will stay 9 inside.
Im not sure why (x^5)^1/3 is equal to x on the outside and x^2 on the inside.

Answer 10

and I messed up y^9 is under the radical.

Answer 11

Ah.

Answer 12

\[\large 1.~\sqrt[3]{72x^{5}y ^{9}} = (72)^{1/3}\cdot (x^5)^{1/3}\cdot y^{9/2}\]

Answer 13

y^9/3?

Answer 14

I keep taking that as a square root instead of a cube root -.-

Answer 15

Yeah, y^(9/3)

Answer 16

I know ... I miss a good chunk of points on a test for that..

Answer 17

So \(x^{5/3}\) can be rewritten as \(x^{1+2/3}\), that means \[\large \sqrt[3]{x^5} = \sqrt[3]{x^2 \cdot x^3}=(x^2)^{1/3}\cdot (x^3)^{1/3} = x^{1+2/3} =x\sqrt[3]{x^2} \]

Answer 18

ohhhhh okay that is so much easier then the book...

Answer 19

Yeah? I like writing them as fractional exponents, then simplifying the fraction, then rewriting it as a radical function.

Answer 20

see our teacher never really taught it like that... he just ran through everything really fast. i mean our final is monday. and a majority of our test had 1-3 chapters on it. and we never would review before the test usually the day before the test we were learning something new.

Answer 21

Ahh... I see.

Does the fractional exponent method make it easier for you?

Answer 22

yeah sorry i got stuck helping someone else an d working on my problems which are so much easier now lol