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

1. Astrophysics

$2\sqrt{16a^4b^2}$?

2. anonymous

Yes.

3. Astrophysics

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?

4. anonymous

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...

5. Astrophysics

$\sqrt{16}=4$

6. Astrophysics

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

7. Astrophysics

Also remember $4^2 = 16$

8. anonymous

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

9. anonymous

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

10. Astrophysics

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 $\sqrt{16} = \sqrt{4 \times 4} = \sqrt{4}\sqrt{4} = 2 \times 2 = 4$

11. anonymous

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

12. Astrophysics

It's ok :P

13. anonymous

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

14. Astrophysics

Yup perfect! Here is a little guide that a user iambatman made for exponents, it may help clear some things up |dw:1439179339225:dw|

15. anonymous

$8b \sqrt{a ^{2}}$

16. anonymous

would it be this?

17. Astrophysics

Not quite, $8a^2b$

18. Astrophysics

Remember it was $\sqrt{a^4}$

19. anonymous

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

20. Astrophysics

I don't quite follow

21. Astrophysics

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

22. anonymous

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

23. Astrophysics

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

24. Astrophysics

Does that make sense?

25. anonymous

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!

26. Astrophysics

When we struggle we learn! And your welcome :)