BrainDen.com - Brain Teasers
• 0

# Powerful rational number?

## Question

Can you find irrational numbers a and b such that ab is a rational number?

## Recommended Posts

• 1
Spoiler

One example of two irrational numbers a and b such that  ab  is rational is where  a = 10  and  b = log(4).
Both  10  and  log(4)  are known to be irrational numbers, yet (√10)log(4) = (10)log(2) = 2, and 2 is definitely rational.

• 1
Spoiler

a = pi

c = a^b = 2

b = ln(2)/ln(pi)

##### Share on other sites

• 0
3 hours ago, bonanova said:

Can you find irrational numbers a and b such that ab is a rational number?

Spoiler

ignore this

Edited by jasen
different view in handphone and computer
##### Share on other sites

• 0

Spoiler

b = sqrt(2).

a = bb

ab = (bb)b = b(bxb) = b2 = 2

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.