Question

Rationalize the denominator and simplify.
https://media.glynlyon.com/g_alg02_ccss_2013/7/q11167.gif

Answer 1

multiply the fraction by \[\frac{\sqrt{7}-2}{\sqrt{7}-2}\]

Answer 2

84

Answer 3

to make things easier, only multiply out the denominator...leave the top as \[12(\sqrt{7}-2)\]

Answer 4

not quite...
\[\frac{12}{\sqrt{7}+2}\frac{\sqrt{7}-2}{\sqrt{7}-2}=\frac{12(\sqrt{7}-2)}{(\sqrt{7})^{2}-(2)^{2}}\]

Can you simplify from there?

Answer 5

I can try

Answer 6

don't worry about the top at first...figure out the bottom and see if it reduces

Answer 7

49 - 4

Answer 8

?

Answer 9

remember, the 7 is being square rooted...so when you square it, it just becomes 7

Answer 10

oh. i don't know how to work out the problem

Answer 11

ok...let's take it a piece at a time...

for any number, a
\[(\sqrt{a})^{2} = a\]

so in your denominator, you have \[(\sqrt{7})^{2} - (2)^{2}\]

using the fact i mentioned at the beginning of the post, that would be \[7-4\]
does that make sense?

Answer 12

yes

Answer 13

good :) so if your fraction is\[\frac{12(\sqrt{7}-2)}{(\sqrt{7})^{2}-(2)^{2}}=\frac{12(\sqrt{7}-2)}{7-4}=\frac{12(\sqrt{7}-2)}{3}\]
all that remains is to reduce the fraction...

Answer 14

yes. 2(sqrt7 -2)/3?

Answer 15

not sure where the 2 came from...12/3 = 4 so the 3 on the bottom cancels and the 12 on top becomes a 4...

Answer 16

i had reduced the 4 also, sorry

Answer 17

so the answer would be 4 sqrt7-2?

Answer 18

that's it...

Answer 19

thank you.