I need help on simplifying radicals, so could someone explain to me how to solve this? 2√16a^4b^2

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I need help on simplifying radicals, so could someone explain to me how to solve this? 2√16a^4b^2

Mathematics
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\[2\sqrt{16a^4b^2}\]?
Yes.
So since it's being multiplied you can split it all up as such \[2\sqrt{16}\sqrt{a^4}\sqrt{b^2}\] can you simplify from there?

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How would you simplify from 16? Because don't you need one number that is a perfect square and the other one not? The only thing I can think of is 4x4 but they're both perfect squares...
\[\sqrt{16}=4\]
\[\sqrt{x} = x^{1/2}\] \[\sqrt{a^4}=(a^4)^{1/2}=a^{4/2}=a^{2}\] do the same with \[\sqrt{b^2}\]
Also remember \[4^2 = 16\]
Okay, so would it be \[8\sqrt{a ^{2}}\]
Because the "b" cancels out because it's b squared?
No, look at what I wrote above, \[\sqrt{x} = x^{1/2}\] this is the same thing, just exponent. \[\sqrt{b^2} = (b^2)^{1/2} \] and for your other question \[\sqrt{16} = \sqrt{4 \times 4} = \sqrt{4}\sqrt{4} = 2 \times 2 = 4\]
I am a moron when it comes to math, so bear with me. Soooo sorry. :/
It's ok :P
So it would just be b? Gosh, exponents really confuse me.
Yup perfect! Here is a little guide that a user iambatman made for exponents, it may help clear some things up |dw:1439179339225:dw|
\[8b \sqrt{a ^{2}}\]
would it be this?
Not quite, \[8a^2b\]
Remember it was \[\sqrt{a^4}\]
So the a goes on the other side of the radical when simplified?
I don't quite follow
Oh, there is no point to put square root sign, a^2 is simplied
It goes outside of the radical/square root when it got simplified from \[a^{4} \to a ^{2}\]?
\[\huge \sqrt{a^4}=(a^4)^{1/2}=a^{4/2}=a^{2}\]
Does that make sense?
Yes, it does. I understand now. Thank you so much! I had a horrible teacher when I took Algebra.. I practically had to teach myself everything, so I struggle a lot. Thanks again!
When we struggle we learn! And your welcome :)

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