Question

rationalize the denominator of 14 divided by 3 + the square root of 2

Answer 1

\[\frac{ 14 }{ 3+\sqrt2 }\] you need to use a conjugate here to get rid of the square root. So..\[\frac{ 14 }{ 3+\sqrt2 }*\frac{ 3-\sqrt2 }{ 3-\sqrt2 }\]\[\frac{ 14*(3-\sqrt2) }{ (3+\sqrt2)(3-\sqrt2) }\]

Answer 2

\[\frac{ 14(3-\sqrt2) }{ 9-3\sqrt2+3\sqrt2-2 }\]\[\frac{ 14(3-\sqrt2) }{ 9-2 }\]\[\frac{ 42-14\sqrt2 }{ 7 }\]

Answer 3

thank you !!

Answer 4

\[\frac{ 42 }{ 7}-\frac{ 14\sqrt2 }{ 7 }=6-2\sqrt2=2(3-\sqrt2)\]

Answer 5

no problem :)

Answer 6

lol I think you did a little bit more than what they asked for

Answer 7

haha, well... simplest form, right? :)

Answer 8

i guess, that's the simplest :P