Question

Dividing Radical Expressions
Simplify.
3/(4+4√5)

Answer 1

multiply and divide by \[4-4\sqrt(5)\]

Answer 2

How do I do that?

Answer 3

do you know what a "conjugate" is?

Answer 4

\[\frac{ 3 }{ 4+4\sqrt{5} }\times \frac{ 4-4\sqrt{5} }{ 4-4\sqrt{5} }\]

Answer 5

\[\left( 4+4\sqrt{5} \right)\left( 4-4\sqrt{5} \right)=?\]
use (a+b)(a-b)=a^2-b^2

Answer 6

\(\bf \cfrac{3}{4+4\sqrt{5}}\cdot \cfrac{4-4\sqrt{5}}{4-4\sqrt{5}}\implies \cfrac{3(4-4\sqrt{5})}{(4+4\sqrt{5})(4-4\sqrt{5})}
\\ \quad \\
recall\implies {\color{blue}{ (a-b)(a+b) = a^2-b^2}}
\\ \quad \\
\cfrac{3(4-4\sqrt{5})}{(4+4\sqrt{5})(4-4\sqrt{5})}\implies \cfrac{3(4-4\sqrt{5})}{(4)^2-(4\sqrt{5})^2}\)