Question

need help with algebra, thanks!

Answer 1

\[\frac{ 4 \sqrt{6} }{ \sqrt{30}} \]

Answer 2

simplify by rationalizing the denominator. Show work

Answer 3

You posted this elsewhere
Multiply the numerator by sqrt(6)

Answer 4

soz - AND numerator

Answer 5

oops! and denominator

Answer 6

so 9.79 is 4 times sqr6?

Answer 7

forget the calculator for now - just multiply top and bottom by sqrt(6)

Answer 8

so it is 4 sqr6 * sqrt6/sqrt30*sqrt6

Answer 9

AND SQRT(6)*SQRT(6) =??

And sqrt (30)*sqrt(6) =??

Answer 10

first: 6
second=13.4

Answer 11

@Darealest123: You do not rationalize the numerator - you rationalize the denominator. So, instead of multiplying by sqrt(6) on both the numerator and the denominator, you will choose to multiply by the radical on the denominator [i.e. sqrt(30)]. And the 13.4 you got earlier is an estimate, which is why we never rationalize the numerator.

Answer 12

forget the calculator - stick with the formula

sqrt(30)*sqrt(6) = sgrt(???)

Answer 13

Do i just multiply the numbers and leave the sqrt

Answer 14

yes

then 180 = 9*4*5

Answer 15

and what do i do with that?

Answer 16

9 and 4 are squares - so you can simplify the sqrt

HOWEVER - @shiraz14 is correct -

Start again and multiply top and bottom by sqrt (30) )(Sorry!)

Answer 17

4 sqrt 6 * sqrt30?

Answer 18

You have missed off the denominator in your above post....


you will still end up with sqrt(9*4*5)

Since 9 and 4 are squares you can simplify

Answer 19

Sooooo... i multiply 9*4 because they are squares

Answer 20

I don't understand what you mean by simplify. If possible when your done you could show me in like bullet points the steps you took because this seems simple but not to me because i don't understand this stuff

Answer 21

No - you multiply by the denominator - to remove the sqrt in the denominator

The top then becomes 4 * sqrt (180)

You then need to look at the factors of 180 - I have done it for you 9*4*5

Sqrt(180)=sqrt(9)*sgrt(4)*sqrt(5)

After simplifying - the only sqrt you are left with is sqrt(5)

Answer 22

so denominator is sqrt 5

Answer 23

?\[4\times \sqrt{180}/ \sqrt{5}\]

Answer 24

@MrNood

Answer 25

You need to do this for yourself to understand it - your post shows that oyu are not thinking about it.

a) multiply top and bottom by sqrt (30)

b) join the 2 sqrt terms on the top into 1

c) factorise the new term on the top

d) Simplify the factors under the sqrt on numerator (I gave you the answer above)

Simplify the 2 sqrt terms in the denominator (they are both sqrt(30))

e) complete the equation

Take it slowly - write the WHOLE equation at all stages

Answer 26

So i multiply both sides by sqrt 30 which would give me 4*sqrt180/189x*sqrt30
then im not sure what to do with the next question

Answer 27

The idea of rationalizing a denominator is to not have any radicals in the denominator.
In this case, some simplification can be done before rationalizing the denominator.

\(\dfrac{4 \sqrt{6}}{\sqrt{30}} \)

First we simplify:

\(= \dfrac{4 \sqrt{6}}{\sqrt{5}\sqrt{6}} \)

\(= \dfrac{4 \cancel{\sqrt{6}}}{\sqrt{5}\cancel{\sqrt{6}}} \)

\(=\dfrac{4}{\sqrt{5}} \)

Now we rationalize:

\(=\dfrac{4}{\sqrt{5}} \times \dfrac{\sqrt5}{\sqrt5} \)

\(=\dfrac{4\sqrt5}{\sqrt{25}} \)

\(=\dfrac{4\sqrt5}{5} \)

Answer 28

so 4sqrt 5/5 is all the way down because you are rationalizing the denominator

Answer 29

Of course, if you didn't realize that you can simplify the fraction before rationalizing, you should arrive at eh same result.

\(\dfrac{4 \sqrt{6}}{\sqrt{30}} \)

\(=\dfrac{4 \sqrt{6}}{\sqrt{30}} \times \dfrac{\sqrt{30}}{\sqrt{30}} \)

\(=\dfrac{4 \sqrt{180}}{\sqrt{900}} \)

\(=\dfrac{4 \sqrt{36 \times 5}}{30} \)

\(=\dfrac{4 \sqrt{36} \sqrt{5}}{30} \)

\(=\dfrac{4 \times 6 \times\sqrt{5}}{6 \times 5} \)

\(=\dfrac{4 \times \cancel6 \times\sqrt{5}}{\cancel6 \times 5} \)

\(=\dfrac{4 \sqrt{5}}{5} \)

As expected, the answer is the same.

Answer 30

Thank you so much you are awesome i gave fan and medal i think :)

Answer 31

Notice that in \(\dfrac{4 \sqrt{5}}{5}\) there is no radical in the denominator. That is the goal of rationalizing a denominator.

Answer 32

You're welcome & thanks.

Answer 33

since @mathstudent55 gave you the answer straight out I assume you have fully understood it now!"