Question

3nth sqrt (x-9)^3

Answer 1

\[(\sqrt[3]{x-9})^3\]

If you cube a cubed root you just remove them both.

\[\sqrt[3]{a^3} = \sqrt[3]{a}^3 = a^{\frac{3}{3}} = a^1 = a \]

Answer 2

its whats inside the radical thats confusing me

Answer 3

x - 9 is just x - 9

Answer 4

Or do I misunderstand your question?

Answer 5

well. i have another problem thats like that and i just dont know what to do with (x-anything)^anything

Answer 6

Just expand it and simplify as much as possible. Unless you have an equal there you can't really solve for x.

Answer 7

so you foil within the radical to expand it?

Answer 8

Well if it's something cubed inside a cubed root, there's no need to foil it cause the two cancel eachother out. Otherwise yeah you'd have to distribute (foil) and hope it turns out nicely.

Answer 9

so the answer is just x-9

Answer 10

Yep.

Answer 11

Assuming that it is as I have it written originally.

Answer 12

thank you, can you help me with sqrt 25(x+2)^4

Answer 13

Of course.

Answer 14

Can you quickly rewrite each of those factors as a square?

Answer 15

25 is what squared?

Answer 16

5

Answer 17

And \((x+2)^4 \) is what squared?

Answer 18

that i dont know

Answer 19

Oh. well what if I asked you what \((2^2)^2\) was. Do you know that?

Answer 20

wouldnt that be 16?

Answer 21

Yes, but don't think about it that way ;p

Answer 22

Think about it as \(2^4\)

Answer 23

When you raise a power to a power you multiply the exponents

Answer 24

Have you been taught this?

Answer 25

the teacher i have sucks. so probably have but not the way your explaining it

Answer 26

Hrm. Ok, well so if raising something to a power multiplies exponents, then taking the root of a power divides the exponent.

Answer 27

For example.

\[\sqrt{5^4} = 5^2\]
\[\sqrt[3]{7^{12}} = 7^4\]
etc.

Answer 28

So if you have

\[\sqrt{a^4} =\ ?\]

Answer 29

okaie. so would (x+2)^4 would just be x+2 ^ 2. and the answer to your question is a^2

Answer 30

Yes precisely. So for your problem you had

\[\sqrt{5^2(x+2)^4} =\ ?\]

Answer 31

well it was 25 which = 5^2.

Answer 32

Right. Same difference, so take the square root of that and you get?

Answer 33

5(x+2)^2

Answer 34

Exactly.

Answer 35

THANKK YOU SO MUCH<!!!!

Answer 36

Very welcome ! =)