How do you simplify #sqrt ((50^2)-4(13+y))#?

1 Answer
ceenik
Apr 24, 2017

#sqrt((50^2)-4(13+y))=2 sqrt(612-y)#

Explanation:

#sqrt((50^2)-4(13+y))#

Order of operations.
Exponents first. #color(red)((50^2))#

#sqrt(2500-4(13+y))#

Next we multiply. #color(red)(-4(13+y))#

#sqrt(2500-52-4y)#

Add or Subtract common variables. #color(red)(2500-52)#

#sqrt(2448-4y)#

Take out common factor 4. This is convenient since 4 has a perfect square root. Whenever you are trying to simplify a square root always look for factors in your numbers like 4, 9, 16, etc... anything with a perfect square root.

#sqrt(color(red)(4)(612-y))#

Complete the square root of 4 and place it outside of the square root.

#color(red) "The 2 is now multiplying the square root."#
#color(red)((2)) (sqrt(612-y))#

So,
#2 sqrt(612-y)#

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