## anonymous 4 years ago Solve the following roots. Please explain the steps.

1. anonymous

$\sqrt{54}$

2. anonymous

$\sqrt{60}$

3. jim_thompson5910

I'll do the first one to get you started

4. jim_thompson5910

The idea is to factor the radicand into two factors where one factor is a perfect square (the largest perfect square possible)

5. jim_thompson5910

Then you break up the root and simplify

6. jim_thompson5910

$\Large \sqrt{54} = \sqrt{9*6}$ $\Large \sqrt{54} = \sqrt{9}*\sqrt{6}$ $\Large \sqrt{54} = 3\sqrt{6}$

7. anonymous

omg thank you so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

8. jim_thompson5910

yw

9. anonymous

So $\sqrt{60}= 3\sqrt{10}$

10. jim_thompson5910

no

11. jim_thompson5910

keep in mind that 60 = 4*15

12. anonymous

So the answer is $2\sqrt{15}$

13. jim_thompson5910

good

14. anonymous

YUS! Victory dance! Thank you so much! You are the most helpful person I have met on here! I cannot thank you enough! I was being made fun of for not being able to do these problems... You changed my life! Literally! Now I won't fail 7th grade! Thank you SO much again! I wish I could give you more medals!

15. jim_thompson5910

yw, glad to be of help

16. anonymous

So I am looking for the biggest possible number to go into it? Like $\sqrt{64} = 2\sqrt{16}$

17. jim_thompson5910

64 is a perfect square

18. jim_thompson5910

since 8^2 = 64 or 8*8 = 64

19. jim_thompson5910

so $\Large \sqrt{64} = 8$

20. anonymous

Ohhh ok! I get it now! Thank you SO much!

21. jim_thompson5910

np

22. anonymous

$\sqrt{72}= 2\sqrt{18}$

23. jim_thompson5910

find the largest perfect square that is a factor of 72

24. jim_thompson5910

the perfect squares (up to 100) are: 1,4,9,16,25,36,49,64,81,100

25. anonymous

So I have to use a perfect square every time?

26. jim_thompson5910

yes, you have to factor the number into two numbers where one number is the largest perfect square possible

27. anonymous

Wow! My mom could never explain as good as you do! lol! I will let you know if I need anymore help! :D Again, I cannot thank you enough! I will forever be in your debt!

28. jim_thompson5910

sure thing, again glad to be of help