Rationalize Denominator

mathxyz · 2024-05-26 09:58:12

I am having a hard time with the following problem:

5 ÷ [cuberoot(2)]

Phrzby Phil · 2024-05-26 14:10:54

What do you need to multiple the denominator by so that it is an integer? Multiple the numerator by the same.

mathxyz · 2024-05-26 18:37:40

Phrzby Phil wrote:

What do you need to multiple the denominator by so that it is an integer? Multiple the numerator by the same.

I will write cuberoot(2) as 2^(1/3).

Do you mean to multiply the top and bottom by 2^(1/3)?

Bob · 2024-05-26 19:44:54

Yes; do it twice so the denominator = 2

Bob

mathxyz · 2024-05-27 02:34:52

Bob wrote:

Yes; do it twice so the denominator = 2
Bob

I did that but my answer is not the book's answer. Can you work it out for me?

Phrzby Phil · 2024-05-27 05:50:49

So, what did you get and what does the book say?

mathxyz · 2024-05-27 06:35:39

Phrzby Phil wrote:

So, what did you get and what does the book say?

My answer is [5•cuberoot(2)]/2.

Book's answer is [5cuberoort(4)]/2.

Bob · 2024-05-27 09:44:55

Let cuberoot(2) be c. Then c^3 = 2

Bob

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