## gfields444 3 years ago simplify 8√63x^5

1. lgbasallote

2. gfields444

no, i'm still very confused on how to even start

3. lgbasallote

$\LARGE \sqrt{63x^5} \implies \sqrt{9 \times 7 \times x^4 \times x}$ does that help?

4. gfields444

a little, the exponents are the things that trip me up the most though.

5. lgbasallote

$\LARGE \sqrt{9 \times 7 \times x^4 \times x} \implies \sqrt 9 \times \sqrt{x^4} \times \sqrt 7 \times \sqrt x$

6. lgbasallote

$\LARGE \sqrt{x^a} \implies x^{a/2}$

7. gfields444

the one before that was too big for the screen lol but let me see if i can keep working this out :)

8. lgbasallote

okay :D

9. gfields444

I got |dw:1343225546659:dw|

10. phi

you can also pull x^4 out of the square root to get $24 x^2 \sqrt{7x}$

11. gfields444

how would it be x^2 outside of the radical and inside it only be x? I need a bit of clarification, I'm not very good at math :/

12. phi

by definition: sqrt(2*2) = sqrt(2)*sqrt(2) = 2 or, in general sqrt(x)*sqrt(x)= x

13. phi

x^5 is short hand for x*x*x*x*x (people don't like typing it out, so they use the short hand) sqrt(x*x*x*x*x) = sqrt(x)*sqrt(x)*sqrt(x)*sqrt(x)*sqrt(x) each pair simplfies to x: x*x*sqrt(x) or, using the short hand x^2 * sqrt(x)

14. phi

Of course, if you do this problem a bunch of times, you start saying things like: if the exponent is even (example: x^4) I can "pull out" x^4 , and divide the power by 2. in other words sqrt(x^4) = x^2

15. gfields444

okay! so all we did when we pulled out 4 from x^5 is divide it by two?

16. phi

the exponent 4 is divided by 2 when you pull x^4 out of a square root. if you have x^5 you write it as x^4 times x. then pull out the x^4 and leave the x inside

17. gfields444

I got it now! :D thank you!