Question

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

Answer 1

\[2\sqrt{16a^4b^2}\]?

Answer 2

Yes.

Answer 3

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?

Answer 4

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...

Answer 5

\[\sqrt{16}=4\]

Answer 6

\[\sqrt{x} = x^{1/2}\]
\[\sqrt{a^4}=(a^4)^{1/2}=a^{4/2}=a^{2}\] do the same with \[\sqrt{b^2}\]

Answer 7

Also remember \[4^2 = 16\]

Answer 8

Okay, so would it be \[8\sqrt{a ^{2}}\]

Answer 9

Because the "b" cancels out because it's b squared?

Answer 10

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 \[\sqrt{16} = \sqrt{4 \times 4} = \sqrt{4}\sqrt{4} = 2 \times 2 = 4\]

Answer 11

I am a moron when it comes to math, so bear with me. Soooo sorry. :/

Answer 12

It's ok :P

Answer 13

So it would just be b? Gosh, exponents really confuse me.

Answer 14

Yup perfect! Here is a little guide that a user iambatman made for exponents, it may help clear some things up

Answer 15

\[8b \sqrt{a ^{2}}\]

Answer 16

would it be this?

Answer 17

Not quite, \[8a^2b\]

Answer 18

Remember it was \[\sqrt{a^4}\]

Answer 19

So the a goes on the other side of the radical when simplified?

Answer 20

I don't quite follow

Answer 21

Oh, there is no point to put square root sign, a^2 is simplied

Answer 22

It goes outside of the radical/square root when it got simplified from \[a^{4} \to a ^{2}\]?

Answer 23

\[\huge \sqrt{a^4}=(a^4)^{1/2}=a^{4/2}=a^{2}\]

Answer 24

Does that make sense?

Answer 25

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!

Answer 26

When we struggle we learn! And your welcome :)