## anonymous 3 years ago Im so lost Can someone please help me with this geomtric mean.. ive started the equation but how to you find the square root? Question BELOW

1. anonymous

$\frac{ 5 }{ x }\frac{ x }{ 12} x^2=60 x=\sqrt{60}$

2. hartnn

huh ? do u just need square root of 60 ?

3. anonymous

yes how to you get the square root?

4. hartnn

can you factor 60 ?

5. anonymous

what does that mean

6. hartnn

like 10=2*5 24=2*2*2*3

7. hartnn

60=...?

8. anonymous

i dont ge it how did you get those numbers

9. hartnn

divide 60 by 2, what u get ?

10. anonymous

30

11. hartnn

so, 60 = 2*30 now 30 is a prime number ? no. so again divide 30 by 2, what u get ?

12. anonymous

15

13. hartnn

so, 60 = 2*2*15 now 15 is a prime number ? no. so again divide 15 by 2, can't divide.... divide 15 by 3, what u get ?

14. anonymous

5

15. hartnn

so, 60 = 2*2*3*5 right ? (since, 5 is a prime number, we stop) are you getting all this ?

16. anonymous

yes right !! & yes i am

17. hartnn

now comes the easy part ... $\sqrt{x.x.y}=\sqrt{x.x}\sqrt y$ so what about $\sqrt{60}=\sqrt{2.2.3.5}=...?$

18. hartnn

i meant $\sqrt{x.x.y}=\sqrt{x.x}\sqrt y=x\sqrt y$

19. anonymous

wow sorry im horrible at math but is it $2\sqrt{15}$

20. hartnn

yes, its absolutely correct :) and you are not horrible at math, you understood all this, means you are good :)

21. hartnn

any doubts ?

22. anonymous

No Doubts!! & Thannk you so much for helping

23. hartnn

welcome ^_^