Question

Will Give Medal To Best Explanation And Answer!

Simplify by rationalizing the denominator

4sqrt6 / sqrt30

Answer 1

I already worked it out, but i want make sure i got it right

Answer 2

\[(4\sqrt{6})/(\sqrt{30}) = (4\sqrt{6)})/(\sqrt{5\times6})=(4\sqrt{6})/\sqrt{5}\times \sqrt{6}=4/\sqrt{5}\]

Answer 3

it is common practice to not leave radicals in the denominator, so multiply by sqrt(5)/sqrt(5)

Answer 4

why cant i multiply the denominator by it self and the numerator?

Answer 5

meaning: why cant i multiply the numerator and denominator by sqrt30?

Answer 6

you can . you get
\[ \frac{4 \sqrt{180} }{30} \]
which can be simplified further

Answer 7

would it change the answer in any way?

Answer 8

if the question is simplify, the way you get to the simplified form does not matter. But you are not done yet.

Answer 9

well all it asks is to simplify, should i keep going to get a completed answer then?

Answer 10

I would factor 180 into 2*90= 2*2*45= 2*2*3*3*5
and pull out a 2 and 3 from the sqrt to get 2*3*sqrt(5)
then simplify

Answer 11

if you multiply by sqrt30/sqrt 30 it will be :

\[(4\sqrt{6})/(\sqrt{30})\times(\sqrt{30})/(\sqrt{30})=4\sqrt{6}\times \sqrt{30}/(30)=4\sqrt{5}/5\]

which's still like what i did

Answer 12

@phi so i get 6sqrt5 when simplified. it doesnt say to solve tho, should i still?

Answer 13

\[ \sqrt{180} = 6 \sqrt{5} \]

your problem is
\[ \frac{4\cdot \sqrt{180}}{30} =\frac{4\cdot 6\sqrt{5}}{30} = \frac{4\sqrt{5}}{5}\]
just like ikarus said.

Answer 14

another way to simplify is if you start with
\[ \frac{4 \sqrt{6}}{\sqrt{30}}= 4 \sqrt{\frac{6}{30} } = \frac{4}{\sqrt{5}}= \frac{4\sqrt{5}}{5}\]

Answer 15

oh ok, i think thats what ikarus said originally. Thanks @phi and @ikarus !

Answer 16

welcome