Question

What is the simplest form of the expression?
Square root 2 minus 6 over 2 plus 6

Answer 1

\[\frac{\sqrt2-6}{2+6}\]??

Answer 2

my guess is it is actually
\[\frac{\sqrt2-6}{\sqrt2+6}\]

Answer 3

\[\sqrt{2}-\sqrt{6}\div \sqrt{2}+\sqrt{6}\]

Answer 4

\[\frac{\sqrt2-\sqrt6}{\sqrt2+\sqrt6}\]

Answer 5

I got \[8-4\sqrt{3}\div8\] is that correct

Answer 6

multiply by the conjugate of the denominator
start with
\[\frac{\sqrt2-\sqrt6}{\sqrt2+\sqrt6}\times \frac{\sqrt2-\sqrt6}{\sqrt2-\sqrt6}\]

Answer 7

seem unlikely
the denominator will be \(2-6=-4\)

Answer 8

would it not be 2+6 on never mind i see my error

Answer 9

your numerator is right

Answer 10

but you can cancel when you get the \(-4\) in the denominator

Answer 11

how

Answer 12

\[\frac{8-4\sqrt3}{-4}\] cancel the \(-4\)

Answer 13

i.e. divide each term in the numerator by \(-4\)

Answer 14

\[-2+\sqrt{3}\]

Answer 15

bingo

Answer 16

ok that makes since thank you

Answer 17

yw