Question

What is the solution to the equation?

Answer 1

\[3^{5}\sqrt{(x+2)^{3}}+3=27\]

Answer 2

@jim_thompson5910

Answer 3

is that 5 for the 3? or is it for the root?

Answer 4

I have no idea... let me screen shot it and post.

Answer 5

alright

Answer 6

Never mind it wont let me screen shot it. its posted all together though.

Answer 7

the thing is that I wonder if it is

\[\Large 3\sqrt[5]{(x+2)^{3}}+3=27\]

notice how the 5 is the index for the radical

Answer 8

I think its supposed to be in the index, because thats how it is in the book, and they talked about the index in our last lesson.

Answer 9

ok so first thing you do is subtract 3 from both sides

Answer 10

from every number?

Answer 11

like this

\[\Large 3\sqrt[5]{(x+2)^{3}}+3=27\]

\[\Large 3\sqrt[5]{(x+2)^{3}}+3{\color{red}{-3}}=27{\color{red}{-3}}\]

\[\Large 3\sqrt[5]{(x+2)^{3}}+0=24\]

\[\Large 3\sqrt[5]{(x+2)^{3}}=24\]

Answer 12

Oh okay! Thats easy!

Answer 13

Now what?

Answer 14

now we divide both sides by 3 to move that "3" on the left side (outside the radical) to the right side

Answer 15

Now divide by 3 on both sides. Then you have both sides to the power of 5.

Answer 16

\[\Large 3\sqrt[5]{(x+2)^{3}}=24\]

\[\Large \frac{3\sqrt[5]{(x+2)^{3}}}{\color{red}{3}}=\frac{24}{{\color{red}{3}}}\]

\[\Large \sqrt[5]{(x+2)^{3}}=8\]

Answer 17

Okay, Got it. Now what?

Answer 18

how do we undo that fifth root? what must we do to both sides?

Answer 19

um...divide them?

Answer 20

not quite

Answer 21

5th powers undo 5th roots

Answer 22

we raise both sides to the 5th power

\[\Large \left(\sqrt[5]{(x+2)^{3}}\right)^{ {\color{red}{5}} }=8^{\color{red}{5}}\]

\[\Large (x+2)^{3} =??\]

Answer 23

uhhh.... 32,768?

Answer 24

yes

Answer 25

\[\Large (x+2)^{3} =32768\]

Answer 26

now we apply the cube root to both sides

\[\Large (x+2)^{3} =32768\]

\[\Large \sqrt[3]{(x+2)^{3}} =\sqrt[3]{32768}\]

\[\Large x+2 =32\]

Answer 27

since \[\Large 32^3 = 32768\] we just take things in reverse to say \[\Large \sqrt[3]{32768} = 32\]

Answer 28

So thats all, right? Because it simplifys to 32?

Answer 29

well x+2 = 32, but we want x itself

Answer 30

x=30?

Answer 31

yes

Answer 32

is that the final answer?

Answer 33

yes

Answer 34

thank you!