Question

How do I simplify 3 sqrt 6 +5 / sqrt 6 + 2

Answer 1

is this correct?
\[3\sqrt{6} + 5 / \sqrt{6} +2\]

Answer 2

am i reading it write is what i mean?

Answer 3

yes. how do i simplify that?

Answer 4

ok, you want to simplify the denominator, do this by multiplying the top and bottom of the equation by the conjugate of the denominator (\[\sqrt{6} - 2\])

Answer 5

Hello @whatwhatt Welcome to Openstudy :)

Answer 6

this will leave you with
\[(3\sqrt{6}+5)(\sqrt{6}-2)\]

Answer 7

all divided by 2

Answer 8

why is it divided by 2?

Answer 9

\[\frac{ (3\sqrt{6}+5)(\sqrt{6}−2) }{ 2 }\]

Answer 10

okay

Answer 11

then you just need to expand the brackets in the numerator

Answer 12

do you know how to do that or did you want me to step you through?

Answer 13

would you please take me through that too?

Answer 14

yeah sure, lemme write it out in my book real quick so i can explain it as clear as i can

Answer 15

i dont really understanding multiplying with radicals

Answer 16

thank you so much!

Answer 17

did you get it @Omistone

Answer 18

\[=\frac{ (3\sqrt{6}+5)(\sqrt{6}-2) }{ 2 }\]
\[= \frac{ 18-6\sqrt{6}+5\sqrt{6}-10 }{ 2 }\]
\[= \frac{18-\sqrt{6}-10 }{ 2 } \]
\[=9-\frac{ \sqrt{6} }{ 2 }-5\]
which = 2.775255129

Answer 19

sorry, that took a really long time to write in the equation writer

Answer 20

thank you so much!

Answer 21

no problem :)
always glad to help with surds