Question

Please correct my work and show your work if I MESSED up please

Answer 1

Hello from MrBillDoesMath!

Answer:

Your answer is correct. (You have earned the unofficial title of Genius, Jr. );

Discussion:

Whew! This is a long problem. Let me see what I get and compare it to your answer. First each of the 3 terms contains the sqrt(yz) so let's factor that terms out. You equations equals

sqrt(yz) (  sqrt(108) +  3 sqrt(98) + 2 sqrt(75) )                           (A)

Hmm....  let's look at the prime factorizations....

108 = 3 * 36 = 3 * (4*9) = 3 * 2^2* 3^2  

98   = 2 * 49 = 2 * 7^2

75   = 3 * 25 = 3 * 5^2

So (A)  =

sqrt(yz)  ( 6 sqrt(3) + 3*7 sqrt(2) +  2*5 sqrt(3) ) =

sqrt(yz)  (  ( 6 + 2*5) sqrt(3) + 21 sqrt(2) ) =

sqrt(yz) ( (6 + 10) sqrt(3) + 21 sqrt(2))  =

sqrt(yz) ( 16 sqrt(3) + 21 sqrt(2) )

Our answers agree!  

Thank you,

MrB