radical expressions: simplify (3 - sqrt[5]) / (3 + sqrt[5])

[keepitreal]

3 - square root 5
_______________
3 + square root 5


I need to simplify it.

 

[Deleted member 4993]

What are you supposed to do? What is the Question?

 

[keepitreal]

I need to simplify it.

 

[Deleted member 4993]

Re: radical expressions

3 - square root 5
_______________
3 + square root 5

I'll do a similar problem:

{A + sqrt(B)}/{C + sqrt(D)} .... multiply the numerator and the denominator by the conjugate of the denominator

= {A + sqrt(B)}/{C + sqrt(D)} * {C - sqrt(D)}/{C - sqrt(D)}

= [{A + sqrt(B)}*{C - sqrt(D)}]/{C^2 - D}

Now multiply out the numerator - FOIL and further simplify.

 

[keepitreal]

Can you use real numbers instead of letters because that really confused me.

 

[Deleted member 4993]

You replace A, B, C and D with numbers and show us how you come out.

 

[keepitreal]

I have no idea.

 

[keepitreal]

7- 3 square root 5
________________
4

 

[Denis]

7- 3 square root 5
________________
4

Close keepi!

(7 - 3sqrt(5)) / 2

 

[Deleted member 4993]

Re: radical expressions

3 - square root 5
_______________
3 + square root 5
\(\displaystyle = \frac{(3 - sqrt{5})}{(3 + sqrt{5})}


= \frac{(3 - sqrt{5})}{(3 + sqrt{5})} X \frac{(3 - sqrt{5})}{(3 - sqrt{5})}


= \frac{(3 - sqrt{5})^2}{(3^2 - 5)}

= \frac{(9 + 5 - 6sqrt{5})}{4}

= \frac{(14 - 6sqrt{5})}{4}

= \frac{(7 - 3sqrt{5})}{2}\)

I need to simplify it.