anonymous
  • anonymous
Solve the following roots. Please explain the steps.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\sqrt{54}\]
anonymous
  • anonymous
\[\sqrt{60}\]
jim_thompson5910
  • jim_thompson5910
I'll do the first one to get you started

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jim_thompson5910
  • jim_thompson5910
The idea is to factor the radicand into two factors where one factor is a perfect square (the largest perfect square possible)
jim_thompson5910
  • jim_thompson5910
Then you break up the root and simplify
jim_thompson5910
  • jim_thompson5910
\[\Large \sqrt{54} = \sqrt{9*6}\] \[\Large \sqrt{54} = \sqrt{9}*\sqrt{6}\] \[\Large \sqrt{54} = 3\sqrt{6}\]
anonymous
  • anonymous
omg thank you so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
jim_thompson5910
  • jim_thompson5910
yw
anonymous
  • anonymous
So \[\sqrt{60}= 3\sqrt{10}\]
jim_thompson5910
  • jim_thompson5910
no
jim_thompson5910
  • jim_thompson5910
keep in mind that 60 = 4*15
anonymous
  • anonymous
So the answer is \[2\sqrt{15}\]
jim_thompson5910
  • jim_thompson5910
good
anonymous
  • 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!
jim_thompson5910
  • jim_thompson5910
yw, glad to be of help
anonymous
  • anonymous
So I am looking for the biggest possible number to go into it? Like \[\sqrt{64} = 2\sqrt{16}\]
jim_thompson5910
  • jim_thompson5910
64 is a perfect square
jim_thompson5910
  • jim_thompson5910
since 8^2 = 64 or 8*8 = 64
jim_thompson5910
  • jim_thompson5910
so \[\Large \sqrt{64} = 8\]
anonymous
  • anonymous
Ohhh ok! I get it now! Thank you SO much!
jim_thompson5910
  • jim_thompson5910
np
anonymous
  • anonymous
\[\sqrt{72}= 2\sqrt{18}\]
jim_thompson5910
  • jim_thompson5910
find the largest perfect square that is a factor of 72
jim_thompson5910
  • jim_thompson5910
the perfect squares (up to 100) are: 1,4,9,16,25,36,49,64,81,100
anonymous
  • anonymous
So I have to use a perfect square every time?
jim_thompson5910
  • jim_thompson5910
yes, you have to factor the number into two numbers where one number is the largest perfect square possible
anonymous
  • 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!
jim_thompson5910
  • jim_thompson5910
sure thing, again glad to be of help

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