Solve the following roots. Please explain the steps.

- anonymous

Solve the following roots. Please explain the steps.

- jamiebookeater

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- anonymous

\[\sqrt{54}\]

- anonymous

\[\sqrt{60}\]

- jim_thompson5910

I'll do the first one to get you started

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## More answers

- 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

Then you break up the root and simplify

- jim_thompson5910

\[\Large \sqrt{54} = \sqrt{9*6}\]
\[\Large \sqrt{54} = \sqrt{9}*\sqrt{6}\]
\[\Large \sqrt{54} = 3\sqrt{6}\]

- anonymous

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

- jim_thompson5910

yw

- anonymous

So \[\sqrt{60}= 3\sqrt{10}\]

- jim_thompson5910

no

- jim_thompson5910

keep in mind that 60 = 4*15

- anonymous

So the answer is \[2\sqrt{15}\]

- jim_thompson5910

good

- 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

yw, glad to be of help

- anonymous

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

- jim_thompson5910

64 is a perfect square

- jim_thompson5910

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

- jim_thompson5910

so \[\Large \sqrt{64} = 8\]

- anonymous

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

- jim_thompson5910

np

- anonymous

\[\sqrt{72}= 2\sqrt{18}\]

- jim_thompson5910

find the largest perfect square that is a factor of 72

- jim_thompson5910

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

- anonymous

So I have to use a perfect square every time?

- jim_thompson5910

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

- 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

sure thing, again glad to be of help

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