Question

Rationalize the denominator of 4 over 6 minus sqrt 7

Answer 1

Hint: multiply top and bottom by \(\large 6+\sqrt{7}\)

this is the conjugate of the denominator

Answer 2

\[24\sqrt{7}\] ?

Answer 3

no but close

Answer 4

\(\large 4(6+\sqrt{7}) = ??\)

Answer 5

24+4sqrt7

Answer 6

better

Answer 7

\(\large (6-\sqrt{7})(6+\sqrt{7}) = ??\)

Answer 8

36-sqrt49?

Answer 9

the square root of 49 is what

Answer 10

7

Answer 11

36-sqrt49

turns into

36 - 7

turns into

29

Answer 12

So the answer is

\[\large \frac{4+4\sqrt{7}}{29}\]

Answer 13

okay, I got it now! Thanks!!!!

Answer 14

yw

Answer 15

ooops i meant to say

So the answer is

\[\large \frac{24+4\sqrt{7}}{29}\]

but you got the idea

Answer 16

can you help me with another?

Answer 17

@jim_thompson5910

Answer 18

sure

Answer 19

3
---
5-6i

Answer 20

Rationalize the denominator

Answer 21

same idea, multiply top and bottom by 5+6i

5+6i is the complex conjugate of 5-6i

Answer 22

15+18i
---------
25-36i

?

Answer 23

close, but the denominator should be 25 - 36i^2

Answer 24

*25-36i^2

Answer 25

good catch

Answer 26

i^2 = -1

25 - 36i^2

25 - 36(-1)

25 + 36

61

So 25 - 36i^2 = 61

Answer 27

so the answer would be 15+18i
----------
61

?

Answer 28

yep

Answer 29

you can break up the fraction if you want, but you're pretty much done

Answer 30

thanks!!

Answer 31

np