Question

What is the solution to the equation?
http://awesomescreenshot.com/0542bbrl7e

Answer 1

I can't tell if it is \[2\sqrt[5]{(x+6)^3}+3=19\]or\[2^5\sqrt{(x+6)^3}+3=19\]

Answer 2

It's the second one

Answer 3

I think...

Answer 4

Yea I think it's the second one because the index would probably be separated from the 2

Answer 5

hmm, lets try that , and see if we get one of the possible options

Answer 6

\[2^5\sqrt{(x+6)^3}+3=19\]

first step is to take 3 away form both sides,

second step is to divide by 2^5

Answer 7

\[2^{5}\sqrt{(x+6)}^3 = 16? \] idk how to divide that...

Answer 8

\[\frac{2^5}{2^5}\sqrt{(x+6)^3}=\frac{16}{2^5}\]

Answer 9

um... woah there... Does the first one cancel itself out? and is the other one 8^6?

Answer 10

8^5*?

Answer 11

yes the LHS simplifies to
\[\sqrt{(x+6)^3}\]
thats why we divided it,

Answer 12

im not sure what you did to the RHS by you might want to simplify 2^5 before simplifying that fraction ,
remember 2^5=2*2*2*2*2

Answer 13

\[\frac{ 16 }{ 32 }?\]

Answer 14

what does LHS and RHS mean? Is it the left and right of something...

Answer 15

Sorry.. I'm not too... aware of my mathematical vocabulary >-<

Answer 16

left hand side of the equation, and right

Answer 17

yeah 16/32, not can you simplify this fraction

Answer 18

now*

Answer 19

Ooooh understood. \[\frac{ 16 }{ 32 }= \div8 = \frac{ 2 }{ 4 } = \frac{ 1 }{ 2 }\]

Answer 20

cool, now you have

\[\sqrt{(x+6)^3}=\frac12\]

Answer 21

now square both sides

Answer 22

o.o I'm not sure how to do that either... >.<

Answer 23

well the square will cancel the square root on the LHS,

Answer 24

and (1/2)^2 = (1^2)/(2^2)=1/(2^2)

Answer 25

I didn't even know there was a sq root on the left hand side... are you talking about the cubed being canceled out? and ... does \[\frac{ 1 }{ 2^2 }\] become the new fraction?

Answer 26

well no

Answer 27

that radical thing is a square root

Answer 28

nvm I don't think cubes is ever canceled out from sq... ohhhh yea... I forgot... does that mean it disappears? \[\left( x+6\right)^3 = \frac{ 1 }{ 1^2 } \] is that what it looks like now... or no?

Answer 29

almost \[\left( x+6\right)^3 = \frac{ 1 }{ 2^2 }\]

Answer 30

now simplify the 2^2 ie 2*2

Answer 31

oops... lol my fault... \[\left( x+6 \right)^3 = \frac{ 1 }{ 4 }\]

Answer 32

good, now get rid of the cube, by raising each side to the power (1/3)

Answer 33

um... \[\left( x+2 \right) = \frac{ 1 }{ 3 } \times \frac{ 1 }{ 4 }\] I'm pretty sure I messed up... and I really don't know where to put the 1/3 on the RHS... or how to raise it at that

Answer 34

1/3x?

Answer 35

>.<

Answer 36

\[\left( x+6 \right)^3 = \frac{ 1 }{ 4 }\\
\left(\left( x+6 \right)^3\right)^{1/3} = \left(\frac{ 1 }{ 4 }\right)^{1/3}\\
x+6= \frac{ 1 }{ 4^{1/3}}\]

Answer 37

Ooooh I see I see... thank you... what happens afterwards? o.o

Answer 38

now take away the 6

Answer 39

...
hmm the answer isn't nice, i think the question must have been

\[2\sqrt[5]{(x+6)^3}+3=19\]Lets try that

taking away the 3 as before
\[2\sqrt[5]{(x+6)^3}=16\]
this time divide by 2

Answer 40

Woah wait I just got so confused >.< do you mean to do the 1/3 thing again then divide by 2? Or just divide everything by 2 instead?

Answer 41

i already took away the +3, because that step was the same as our first attempt

Answer 42

from \[2\sqrt[5]{(x+6)^3}=16\] just divide by 2

Answer 43

\[^{5}\sqrt{x+3}^{3} = 8\] ...

Answer 44

why did the 6 become a 3?

Answer 45

I divided it by 2 >.<

Answer 46

/: I have to go in 2 minutes

Answer 47

the 2 out the front was a factor, and when you divide you only have to divide one on the factors , so the six stays as a six

Answer 48

5^√(x+6)^3=8

now get rid of the 5root by raising each side to the power 5
and get rid of the ^3 by raising each side to the power (1/3)

Answer 49

Well nvm I'm good... but... \[\sqrt{x+6} = (8)^{1/3}\]

sorry... I'm stuck >.<

Answer 50

that is good, but you forget to leave the little 5 on the radical

\[\sqrt[5]{x+6}=8^{1/3}\]

Answer 51

now you can rewrite that fifth root like this

\[\sqrt[5]{x+6}=(x+6)^{1/5}=8^{1/3}\]
now to clear it off the LHS raise both sides to the power 5
\[((x+6)^{1/5})^5=(8^{1/3})^5\]
and simplify

Answer 52

I'm not sure how to simplify that... does it turn into x + 6 = on the lhs?
I don't know how to deal with the exponents on the rhs though...

Answer 53

yeas,


for the RHS

just remember the index rule that; (a^n)^m=a^(nm)

Answer 54

\[x + 6 =8^{(1/3)(5)}\] ?

Answer 55

Thank you for working so far with me btw

Answer 56

yeah and you can simplify that rhs (1/3)(5)=5/3