Strangest radical problem ever: Trying for over an hour

december12

New member
Joined
May 14, 2016
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1
I have googled and been trying to simplify this problem for over an hour.

1
_______
√7 + 1

So far I multiplied the numerator and denominator by √7, getting: √7
_______
7 + √7

How would I simplify this? Google says the answer is: √7 - 1
_______ but I have no idea how to get there. Nothing I have tried has worked.
6
 
As a hint for how to proceed, consider the expression a2 - b2. What do you get when you factor that? Now suppose that we let a=sqrt(7) and b=1. What do you notice about the factors? How does that relate to the given problem?
 
I have googled and been trying to simplify this problem for over an hour.

1
_______
√7 + 1

So far I multiplied the numerator and denominator by √7, getting: √7
_______
7 + √7

How would I simplify this? Google says the answer is: √7 - 1
_______ but I have no idea how to get there. Nothing I have tried has worked.
6


Multiply the given fraction by:

\(\displaystyle \dfrac{\sqrt{7} \ - 1}{\sqrt{7} \ - 1}\)

to eliminate the radical denominator.
 
I have googled and been trying to simplify this problem for over an hour.

. . . . .\(\displaystyle \dfrac{1}{\sqrt{\strut 7\,}\, +\, 1}\)

So far I multiplied the numerator and denominator by √7, getting:

. . . . .\(\displaystyle \dfrac{\sqrt{\strut 7\,}}{7\, +\, \sqrt{\strut 7\,}}\)

How would I simplify this? Google says the answer is:

. . . . .\(\displaystyle \dfrac{\sqrt{\strut 7\,}\, -\, 1}{6}\)

but I have no idea how to get there. Nothing I have tried has worked.
To learn the basic process (called "rationalizing" a radical denominator), try here. ;)
 
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