Question

what is equivalent to:

(3+5(radical3) / (4-2(radical3)

*please show steps*

Answer 1

You would have to rationalize the denominator

Answer 2

ok, continue?

Answer 3

\[\frac{ 3+5\sqrt{3} }{ 4-2\sqrt{3}}\] So you would multiply the numerator and the denominator by conjugate of \[4 - 2\sqrt{3}\]

Answer 4

Do you know how to find the conjugate?

Answer 5

yes i think can you explain more please

Answer 6

so the conjugate would be
\[4+2\sqrt{3}\]
multiply both sides by that and you get
\[\frac{ (3+5\sqrt{3})(4+2\sqrt{3}) }{ (4-2\sqrt{3})(4+2\sqrt{3}) }\]

Do you think you could simplify that more?

Answer 7

i think so?

Answer 8

so it would be:

\[\frac{ 12+6\sqrt{3}+20\sqrt{3}+10\sqrt{9} }{ 16+8\sqrt{3}-8\sqrt{3}-4\sqrt{9} }\]

right?

Answer 9

yeah. Can you simplify the radicals/cancel anything out?

Answer 10

then it would be:

\[\frac{ 12+26\sqrt{3}+30 }{ 4 }\]

right?

Answer 11

yeah, you need to add 12 and 30 too.

Answer 12

so it would be:

\[\frac{ 42+26\sqrt{3} }{ 4 }\]

Answer 13

Yeah, you've got it!

Answer 14

is there a way to simplify it more?

Answer 15

divide the top and bottom by 2

Answer 16

can you divide \[26\sqrt{2}\] by 2

Answer 17

yes, its just\[13\sqrt{3}\]

Answer 18

so would it be:
\[\frac{ 21+13\sqrt{3} }{ 2 }\]

Answer 19

and that's it?

Answer 20

Yes

Answer 21

ok thank you!

Answer 22

No Problem :)