Question

simplify the radical -4sqrt 6x^5y^6 * 7 sqrt 8x^3y show work

Answer 1

\[-4\sqrt{6x^5y^6}*7\sqrt{8x^3y}\]

Answer 2

Is that the question ^^^ ?

Answer 3

yes that is the question

Answer 4

when multiplying radicals, you can combine them like this:
\[\sqrt{a}*\sqrt{b}=\sqrt{a*b}\]

Answer 5

ok and how do i do that if they are different

Answer 6

so, we can rewrite as below
\[-4*7*\sqrt{6*8*x ^{5+3}*y ^{6+1}}\]

Answer 7

is the above clear ?
what do you mean "if they are different" ?

Answer 8

ok i see what you did now what do i do next

Answer 9

next: rewrite as below:
\[-28*\sqrt{3*4^2*x^8*y^7}\]

Answer 10

so it should read \[-28\sqrt{48x^8y^7}\]

Answer 11

oh okay

Answer 12

nevermind what i got i just multiplied everything

Answer 13

ok what do i do after i get what you have

Answer 14

next

\[-28*4*\sqrt{3}*\sqrt{x^8}*\sqrt{y}*\sqrt{y^6}\]

Answer 15

what do i do after that

Answer 16

\[-112*\sqrt{3}*x^4*y^3*\sqrt{y}\]

Answer 17

that's about as far as you can go here.

Answer 18

you could also write it like this:
\[-112*\sqrt{3}*x^4*y ^{\frac{7}{2}}\]

Answer 19

Is it all clear ? If not let me know where it is not :)

Answer 20

not sure where you got-112 from

Answer 21

from -28*4

Answer 22

oh ok
and what about the other things

Answer 23

Remember we had this number inside the radical ?

\[\sqrt{48}=\sqrt{3*4^2}=\sqrt{3}*\sqrt{4^2}=\sqrt{3}*(4^{2})^{\frac{1}{2}}=\sqrt{3}*4\]


the -112 came from:
-7*4 (which were always outside the radicals) * 4 (that's the 4 from above, taken out of the radical)

Answer 24

ok what about \[\sqrt{3}*x^4*y^3*\sqrt{y}\] what do i do with these ad how did you get them

Answer 25

you can't do much more with these.

The way I got them, is in the history of posts I made above.
We can review them one by one, to make sure they are all clear.


If you want to remove radicals completely from
the expression you can convert like this:
\[\sqrt{x}=x ^{\frac{1}{2}}\]

Do yo want to do that ?

Answer 26

can we go through each separately

Answer 27

sure.
The first thing was to combine the two radicals into one long one (see my 3rd and 4th post above).

Answer 28

ok i got that

Answer 29

If you look at the expression in the 4th post, you will see that x and y have powers that are sums of two numbers. Do you see why that is ?

Answer 30

i dont really understand it

Answer 31

How much is:
x^2*x^3=?

Answer 32

x^5

Answer 33

right,
x^2*x^3=x^(2+3)=x^5

And how much is:
x^5*x^3=?

Answer 34

x^8

Answer 35

how much is:
\[\sqrt{x^5}*\sqrt{x^3}\]

Answer 36

hint: combine into one radical.

Answer 37

\[\sqrt{x^3}*x^5\]

Answer 38

like that

Answer 39

It should be like this:
\[\sqrt{x^5}*\sqrt{x^3}=\sqrt{x^5*x^3}=\sqrt{x ^{5+3}}=\sqrt{x^8}=(x^8)^{0.5}=x^{8*0.5}=x^4\]

Answer 40

I broke it into lots of steps on purpose ... go over it and let me know if it is all clear.

Answer 41

there are 7 steps above. let me know if any of them is unclear.

Answer 42

what is after \[(x^8)^{0.5}=x^8\] i cant see it

Answer 43

The last part is:
\[(x^8)^{0.5}=x^{8*0.5}=x^4\]

Answer 44

can i email you a link and you actually show me how we are doing this because i think i have confused myself

Answer 45

ok

Answer 46

post the link here

Answer 47

ok here it is http://www.twiddla.com/605550

Answer 48

no unwanted people please