Question

Convert V=x^3 to x=...?

Answer 1

solving for x instead?

Answer 2

Yes

Answer 3

You want to isolate the x, to "undo" the cube, you have to take the cube root of both sides. Can you tell me what you can?

Answer 4

what you get*

Answer 5

What would taking the cube of both sides look like though?

Answer 6

\[\large \sqrt[3]{V} = \sqrt[3]{x^3}\]

Answer 7

When you take the cube root of x, it turns into : \[(x^3)^{1/3} = x^{3 \cdot 1/3}\]

Answer 8

and what is \[3 \cdot \frac{1}{3}\]

Answer 9

1

Answer 10

Good :)

Answer 11

So what would be your answer?

Answer 12

I'm honestly still confused. Would it be just the 3 square root V?

Answer 13

Yes it would :)

Answer 14

What's confusing you?

Answer 15

Basically, if we are given an equation ans we are solving for one variable in place of the other, we want to "isolate" the variable we are solving for.

Answer 16

In this case, x was raised to the power of 3, so we had to "undo" its power to get it all by itself.

Answer 17

and the only way to "undo" \(x^3\) is to take it's inverse power, which is \(\large \sqrt[3]{x}\)

Answer 18

Ohhh ok, I was confused about the x part, but now I get it... I have one more problem, can you help me with it?

Answer 19

And that is why you got x o the power of 1, because \(3 \cdot \frac{1}{3} = 1\)

Answer 20

Sure thing :)

Answer 21

Thank you! So the square root of a^2+b^2=c

Answer 22

And we are solving for a

Answer 23

Ok, you want to isolate a^2 on the left side of the equation first, how would you do that?

Answer 24

Wouldn't you square both sides first to get rid of the square root?

Answer 25

Nope, that would make the left side more complicated to solve than need be, try again :P

Answer 26

Subtract b^2?

Answer 27

Good :)

Answer 28

And what do you get?

Answer 29

a^2=c^2-b^2

Answer 30

Good:)

Answer 31

Now you can take the square root of both sides, just like your previous problem, "undo" the square on a^2.

Answer 32

Wait, was I supposed to have c^2?

Answer 33

oh no, you don't need to square that. You just leave the c term as i is.

Answer 34

it*

Answer 35

So would it be a=square root of c-b^2, or would you take the b^2 out?

Answer 36

Yes :)

Answer 37

You don't need tot take the b out.