Question

simplify?

Answer 1

\[6\sqrt[4]{2}-14\sqrt[3]{2}+5\sqrt[3]{2}+7\sqrt[4]{2}\]

Answer 2

Do you know how to convert to exponents? This is the only way you can solve this.

Answer 3

no

Answer 4

@IMStuck

Answer 5

For example,\[\sqrt[3]{4}=(4)^{\frac{ 1 }{ 3 }}\] Look familiar?

Answer 6

oh yeah it does

Answer 7

Ok, that's good. The first one is\[6\sqrt[4]{2}\]In exponential form that is\[6(2)^{\frac{ 1 }{ 4 }}\]You could figure this out on your calculator. Do you know how?

Answer 8

no

Answer 9

Ok, let me show you. Give me a sec; I'm trying to find the other way to do this that does not use your calculator, just in case you're not allowed to on a test or whatever. Can you hang out for a sec and wait for me?

Answer 10

i can use a calculator

Answer 11

Ok that's very cool because I dont know for sure that you could do this otherwise. Look back at what I typed in for the first term. \[6(2^{\frac{ 1 }{ 4 }})\]Enter 2 in your calculator and then hit the ^ button and then 1/4. Tell me what you get.

Answer 12

16384

Answer 13

@IMStuck

Answer 14

Oh my...sorry I was gone so long. I'm back now. 2^1/4 power equals .5. Try it again.

Answer 15

still not getting that

Answer 16

Ok, before I go on, does it say in what form to leave your answer?

Answer 17

in the radical form?

Answer 18

Does it say that?

Answer 19

no but thats what all the answers are in

Answer 20

Ok, then that changes everything!! Makes it easier on us! Yay for easy! Do you know the rules for adding and subtracting radicals?

Answer 21

kinda

Answer 22

You can only add and subtract radicals that have the same index. That means you can only add and subtract square roots with/from square roots; you can only add/subtract cube roots with/from cube roots; 4th roots with 4th roots, 5th roots with 5th roots, etc. In our expression above we have two terms that have a 4th root and two terms that have a cube root. We can combine the cube roots and then combine the 4th roots because they are "like". So let's rearrange this to say\[6\sqrt[4]{2}+7\sqrt[4]{2}-14\sqrt[3]{2}+5\sqrt[3]{2}\]Now the "like terms" are next to each other and we can add or subtract them. Any ideas what to do with these?

Answer 23

add the like terms

Answer 24

You add the 6 and the 7 to get 13 and then keep the radical \[13\sqrt[4]{2}\]Try the next ones now.

Answer 25

\[19\sqrt[3]{2}\]

Answer 26

Isn't that a negative 14, though?

Answer 27

wow not to butt in, but you need to know nothing about exponents to do this
combining like terms in \[6\sqrt[4]{2}-14\sqrt[3]{2}+5\sqrt[3]{2}+7\sqrt[4]{2}\] is exactly the same as combining like terms in
\[6x-14y+5y+7x\]

Answer 28

just add up the like terms is all

Answer 29

I know; that's why I asked him/her in what form the answer is to be. but thanks for the input.

Answer 30

\[-9\sqrt[3]{2}\]

Answer 31

Yep that's right1 Now put your two answers together in one expression and you're good to go! Good job! Always remember that you have to have like indexes in order to add or subtract.

Answer 32

\[13\sqrt[4]{2}-9\sqrt[3]{}\]

Answer 33

2