Proving certain radicals are irrational

putongren · September 12th, 2017, 10:45 PM

Prove $\displaystyle \sqrt{2} + \sqrt{3}$ is an irrational number.

My attempt to solve this problem is to equate $\displaystyle \sqrt{2} + \sqrt{3}$ to $\displaystyle \frac{a}{b}$ and show that a or b cannot be integers. I don't know how to do that.

romsek · September 12th, 2017, 10:53 PM

https://math.stackexchange.com/quest...-is-irrational

September 12th, 2017, 10:45 PM	#1
putongren Newbie Joined: May 2015 From: San Francisco Posts: 2 Thanks: 0	Proving certain radicals are irrational Prove $\displaystyle \sqrt{2} + \sqrt{3}$ is an irrational number. My attempt to solve this problem is to equate $\displaystyle \sqrt{2} + \sqrt{3}$ to $\displaystyle \frac{a}{b}$ and show that a or b cannot be integers. I don't know how to do that.
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September 12th, 2017, 10:53 PM	#2
romsek Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,410 Thanks: 715	https://math.stackexchange.com/quest...-is-irrational
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