Language of Mathematics II (48): Reducing Radicals

[chaospoet]

OK there's something I'm not quite getting: why is there still a cubed root in the final answer? If you've "paid the toll", as you put it, why is it still there? Why isn't the final answer 10a cubed, b, to the square root of 4a squared with the radical gone? I just keep expecting, for the sake of balance on both sides of the equal sign, for it to be gone. I don't understand why it's still there. I seem to be missing something in the logic of the equation here.

[chychochycho]

the cube root symbol is still there because everyone that was inside couldn't come out. The only way you can come out is to group yourself with three identical things. If you can't group into threes then you can't come out. And if there is anything that can't come out, then the cube root symbol stays. Those numbers and variables inside are stuck until they can group in threes.

hope that makes sense?

[chaospoet]

@chychochycho I think I got you. So this isn't like fractions for example where after you break things down into their prime factors you cross cancel like terms? I think that's what's confusing me. I keep thinking if you have a radical of 3 outside the root and you have say 5 of something (a to the power of 5) that three of those would cancel out the cubed radical outside the root symbol so you'd just end up with a root symbol with a 2 inside of it. That's what I keep expecting.

[chychochycho]

Yap, now you got it. It's NOT like division where you cancel terms. The 3 stays there, it's attached to the root symbol. The only time you don't write the cube root (the whole symbol) is when there is nothing left inside of it, so you don't need it anymore. Easy as pie :)

[MistaThrill]

im a straight A student ive never had to study things just came to me.... this didnt but u explained it in a way i can understand THX

[chychochycho]

glad to help :)

[skatezombie808]

that's what im SAYIN! why can't they just talk NORMAL like this guy?? jeez.. math jargon is so ridiculous.

oh, thanks again chycho.

[Timzsk8]

Thanks Chycho!!! I'm so glad I suscribed!

[chychochycho]

me too, and it's definitely my pleasure :)

[liangqiaokajia]

love your vids! I forced all my friends in Geometry to watch ur videos and all of them said it was very helpful! thanks a lot!

[chychochycho]

my pleasure, glad it helps :)