Question

Please help!! (4√5+7√15)/(6√15-√5) Rationalize the denominator.

Answer 1

Multiply the numerator and denominator by the conjugate of the denominator, which would be (6√15+√5)

Answer 2

(4√5+7√15)/(6√15-√5)*(6√15+√5)(6√15+√5)?

Answer 3

yes basically. so top and bottom would be multiplied by the same thing

Answer 4

(4√5+7√15)/(6√15-√5) * (6√15+√5)/(6√15+√5

Answer 5

\[\frac{ 4\sqrt{5} + 7\sqrt{15} }{ 6\sqrt{15} - \sqrt{5} } \times \frac{ 6\sqrt{15} + \sqrt{5} }{ 6\sqrt{15} + \sqrt{5} } \]

Answer 6

ranga's visual is very helpful

Answer 7

How do you multiply if √5 and √15 are not the same? I'm not understanding that part.

Answer 8

Would I need to make them the same or leave them alone?

Answer 9

\[\sqrt{5} \times \sqrt{15} = \sqrt{5 \times 15} = \sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}\]

Answer 10

multiply what is under the radical

Answer 11

For rationalizing the denominator use the formula (a + b) x (a - b) = a^2 - b^2

Answer 12

For 4√5 and 6√15 do I multiply the 4 and 6 together?

Answer 13

yup

Answer 14

24√75 would simplify to 120√3

Answer 15

So for the numerator would be 24√75 +20 +42√225 +7√75 without being simplified?

Answer 16

correct

Answer 17

And the denominator would be (6√15)^2 (√5)^2 ?

Answer 18

with a minus sign in between

Answer 19

(6√15)^2-(√5)^2

Answer 20

yes

Answer 21

Then do I combine like terms in the numerator?

Answer 22

yep

Answer 23

31√75+20+42√225?

Answer 24

simplify the denominator too. You will get a nice round number without all the radicals. That is the whole idea behind multiplying by the conjugate pair.

Answer 25

How do I do that exactly?

Answer 26

well your denominator should have the 6√15^-√5^2. so with those numbers, you can make them simpler.

Answer 27

(6√15)^2-(√5)^2 = (36)(15) - (5)

Answer 28

I'm not following. Sorry.

Answer 29

(ab)^2 = (a^2)(b^2)

The radical sign here is the square root. If you take the square root of a number and then square it the square root and the square will cancel out and you will be left with the number.
So if you square (square root of 15) you will be left with 15.

Answer 30

Okay. I got it but I'm still not understanding the simplifying the numerator.

Answer 31

\[\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}\]

Answer 32

So for 24√75 I would multiply the 5 and the 24 together?

Answer 33

yes

Answer 34

So √225 would be 75√3?

Answer 35

or just 15

Answer 36

How did you get the 15?

Answer 37

42√225 would be 42(15)

Answer 38

the square root of 225 is 15

Answer 39

120√3+20+15?

Answer 40

120√3+20+(42)(15) + 35√3 should be in your numerator.

Answer 41

I have not double checked my numbers but I am getting
\[\frac{ 634 + 155\sqrt{3} }{ 535 }\]

If OCity gets the same that would be like double checking!

Answer 42

I've got the same!

Answer 43

Cool!

Answer 44

I get it. Thanks guys!

Answer 45

you're welcome :)

Answer 46

yw

Answer 47

There isn't a way to give you both a best response is there?

Answer 48

no, go ahead and give it to ranga, he provided the most help, i was the backup :)

Answer 49

: ( It is saying the answer is wrong.

Answer 50

But it looks right.

Answer 51

let me check the math

Answer 52

does it give you 155√3 + 650/535 instead?

Answer 53

I don't think so. I think it wants it more simplified or something..

Answer 54

In the example it gives it is talking about canceling the common factor.

Answer 55

155√3/535+130/107

Answer 56

we already did that. but i see the error now. earlier, the answer that was arrived at was 634, not 650. I'm getting 650 now

Answer 57

It's not wanting to take the 650 either.

Answer 58

I hate this math program. It is so picky.

Answer 59

:/ that's strange..I'm not sure how to simplify that further than the two fractions with a common denominator of 535

Answer 60

Do you want to see if I can send you the example using a screen pic?

Answer 61

sure

Answer 62

http://tinypic.com/view.php?pic=34rawwh&s=5#.Ultx3xAwIyE

Answer 63

Sorry that took so long.

Answer 64

ohhh i see what they mean. okay

Answer 65

Are you needing the rest of it?

Answer 66

no, i think i got it.
all the numbers in our solution can be divided by 5. so,
155√3+650/535 would simplify to 31√3+130/107

Answer 67

5 is the common factor of the solution

Answer 68

So 31 and all of that all over 107 right?

Answer 69

yup

Answer 70

Thank you!

Answer 71

not a problem! :)

Answer 72

It's right! Woot!

Answer 73

:D