SOLUTION: Find the square root of 32-6√15

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Question 1152514: Find the square root of 32-6√15
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Consider this calculation:



=

So if you have an expression in the form , then its square root is .

To find the square root of the given expression, you need to put it in exactly that form -- specifically, you need the radical part to be . So



And then the task is to find the numbers a and b for which a+b=32 and ab=135.

Those numbers are 27 and 5, so
Answer by ikleyn(52847)   (Show Source): You can put this solution on YOUR website!
.

The key step is to notice (or to derive) that


    32 -  = .    (1)


Indeed, square the binomial  ,  using the formula    =   with a =   and  b = .


As soon as you established it, only one step remained to the answer:


    the square root of   is the square root of the right side of (1),  which (i.e. the square root)  is  .    ANSWER


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