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Mathematics 6 Online
EndersWorld:

Find the product or quotient.

EndersWorld:

\[(\sqrt[4]{6})(\sqrt[3]{6})\]

EndersWorld:

Then for my first step I got

fall15:

Hmm give me some time to solve it out on paper.

EndersWorld:

\[6\frac{ 1 }{ 4 } * 6\frac{ 1 }{ 3 }\]

mLe:

hmm have you seen something like \( \large x^2 * x^3 = x^5\) before?

fall15:

6^(7/12) is your answer I think.

mLe:

@fall15 I believe EndersWorld has a deeper misunderstanding seeing that they thought 6 1/4 * 6 1/3 would be the second step perhaps if we gave them an explanation, it would help them with their other homework questions as well

EndersWorld:

@mLe yes I have, but I have a different formula to use, would you like me to give it to you?

EndersWorld:

fall15:

|dw:1523918049764:dw|

fall15:

Sorry took me some time to draw it.

EndersWorld:

^that looks like how my teacher did it

fall15:

Do you understand what I did?

EndersWorld:

Yes! I just need someone to walk through it with me, I’m a little slow

mLe:

ohhhh right right right I misread that you wrote 6 1/4 as in 6.25 rather than 6^(1/4) as an exponent @ EndersWorld and awesome @ fall15 , I really like how you did that :)

EndersWorld:

I have a couple I need help with a couple I need y’all to check, do y’all have a few?

fall15:

|dw:1523918271155:dw|

fall15:

That should help you to understand how it works. It's a bit messy though. . .

EndersWorld:

I get it.

fall15:

Great!

mLe:

cool, what else can we help you with? :D

EndersWorld:

I have five questions I need someone to check, and then I need help with 4 others

EndersWorld:

Can y’all help?

fall15:

I'll try. Post them.

EndersWorld:

\[(36)^1/2\]

EndersWorld:

That’s 36 with a exponent of 1/2

EndersWorld:

Then I got square root of 36, then 6 as a final answer

fall15:

Yeah it's correct. Good job ender.

EndersWorld:

2^1/2 * 32^1/2 square root of 2 * square root of 32 Then I got \[\sqrt{6^4}\] Then got 6 as a final answer once again

fall15:

hmm it's not right

fall15:

It's 8

EndersWorld:

Hmmm...

EndersWorld:

I’m confused..

EndersWorld:

Square root of 6 is.... uh... nvm

Angle:

\(\large \sqrt{2} * \sqrt{32} = \sqrt{2*32}\)

EndersWorld:

OOOOOO so, square root of 64=8?

fall15:

You got it!

EndersWorld:

8^2/3

EndersWorld:

\[\sqrt[3]{8^2}\]

EndersWorld:

\[\sqrt[3]{64} =4\]

Angle:

perfect :)

EndersWorld:

x^1/6= \[\sqrt[6]{x}\]

fall15:

Correct.

EndersWorld:

x^2/7=\[\sqrt[7]{x^2}\]

fall15:

correct

EndersWorld:

Are you good with exponential form?

fall15:

Let me take look. Post them.

EndersWorld:

Square root of -10 I got 3.9e-7 somehow...

fall15:

You should be using imaginary numbers. . .

Angle:

interesting... I don't believe it is possible to get a square root of a negative number (you would get imaginary numbers)

fall15:

i should be in your answer. . .

EndersWorld:

Hmm.. oo I got 3.9i the first time... thought I was wrong

fall15:

The letter i

Angle:

are you asked to estimate it? I feel like you could probably keep the square root 10

fall15:

No no no that's wrong. It's intended that way for a purpose.

fall15:

i= -1

fall15:

give me a second to draw it all out and post it for you

EndersWorld:

EndersWorld:

Straight off my homework paper^

fall15:

|dw:1523920196164:dw|

fall15:

YOu could keep the i inside with the 10 but it's not a proper answer that makes sense then so you write the i outside of the square root.

EndersWorld:

How would that be in exponential form though?

EndersWorld:

I have one more exponential form question... and it has a variable in it...

fall15:

|dw:1523920390315:dw|

fall15:

That's how you would write in exponential form. ^

Angle:

hmm

Angle:

but the i is not in the square root

fall15:

That's right. It shouldn't be.

Angle:

|dw:1523920507957:dw|

fall15:

Yeah that's how it's done.

fall15:

but no the i should be 10 i with the 1/2

EndersWorld:

:thonk: my head hurts...

fall15:

|dw:1523920595347:dw|

Angle:

i = (-1)^(1/2) by itself, so i in the final answer should not be in the parenthesis

EndersWorld:

\[\sqrt{(7x)^3}\]

EndersWorld:

One does not simply put THAT in exponential form...^

fall15:

I'm honestly losing track. . .

Angle:

it's the same idea \(\large \sqrt{x} = x^{1/2} \) so \(\large \sqrt{(7x)^3} = ( ~(7x)^3~)^{1/2}\)

EndersWorld:

Me too,... thank you guys so much! <3 sadly I have to go... I guess I’m leaving 3/10 unanswered XD, I got chores to do!

Angle:

wait, I wasn't done ;-;

fall15:

tbh most of this stuff is old for me. I barely remember some of it. so angle could be right or wrong. I have no idea. All I know is that there should an i and a 10 with 1/2 as the exponent.

Angle:

there is \(\large (x^2)^3 = x^{2*3} = x^6\)

Angle:

so \(\large \sqrt{(7x)^3} = ( ~(7x)^3~)^{1/2}\) becomes \(\large (7x)^{3*(1/2)} = ~?\)

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