Question

Please Help how can you write the expression with a rationalized denominator? 4+3^sqrt 3 / 3^sqrt 6

Answer 1

@campbell_st @mathmale can you help

Answer 2

Can u draw out the problem?

Answer 3

yes

Answer 4

That looks confusin^

Answer 5

\[\frac{ 4+\sqrt[3]{3}}{ \sqrt[3]{6} }\]

Answer 6

can you help

Answer 7

@nikato

Answer 8

DB: Thanks for typing this problem into the Equation Editor. SO much easier to read that way. Your task here is to rationalize the den., which means you must eliminate that radical from the denom. Have you done this kind of problem before?

Answer 9

DB: I'm glad to help you and enjoy helping you, but I do expect to have your full attention during the process. Please respond.

Answer 10

To simplify multiply top and bottom by ur denominator

http://www.purplemath.com/modules/radicals7.htm

Answer 11

DB: Open Study has tattled on you. It says you're "just looking around" (not paying attention to the solution of this problem. DB??

Answer 12

yes

Answer 13

DB: your task is to eliminate that radical from the denominator.
Your current denominator is 6^(1/3), right?

Answer 14

yes

Answer 15

6 is not a perfect cube, is it? Our task is to find a multiplier for 6 that transforms it into a perfect cube. Does this sentence make sense to you, and, if so, do you know what to do next?

Answer 16

we need to find the number clothes to 6 that is a perfect cube

Answer 17

Not closest to 6, but a number, when multiplied by 6, results in a perfect cube. Sorry, this is a bit abstract and I will have to think for a moment myself to determine what such a number would be. Would you try doing the same thing?

Answer 18

yes

Answer 19

I found 6^3. Just to speed the process

Answer 20

So, DB, if you multiply that 6 by 36 (courtesy of nikato), what do you get, and is that result a perfect cube?

Answer 21

yes its 216

Answer 22

Good, and is 216 a perfect cube?

Answer 23

yes

Answer 24

Soooo cooool.
Now go back to that expression you so beautifully typed in the Equation Editor. Multiply both numerator and den. by 36. Note how the den. becomes a perfect cube?

Answer 25

yes

Answer 26

So, DB, your denom is 216 and the cube root of that is 6.
Your numerator is (4+third root of 3)(36). Write the answer to this problem as

cube root of (4+third root of 3)(36)/6. that's it. We're rationalized the denom.

Answer 27

thanks can you help with one more

Answer 28

Can't promise; I'm in the midst of helping another student with a different problem and would like to hit the sack soon. But please post your next question; either I or someone else will respond.