How do you simplify 2 squareroot of 27 minus square root of 75 plus square root of 24?

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Answer 1 · 2016-02-18T21:05:14

#sqrt(3)color(white)(.) (1+2sqrt(2))#

#color(blue)("Given: "2 xxsqrt(27)-sqrt(75)+sqrt(24)#

Note that simplify is not 'solve'
Looking for a common factor I have spotted #sqrt(3)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider:
# sqrt(27)" "=" " sqrt(3xx3xx3)" "=" "sqrt(3xx3^2)" " =" " 3sqrt(3)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider:
#sqrt(75)" "=" "sqrt(5xx15)" "=" "sqrt(3xx5^2)" "=" "5sqrt(3) #

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider:
#sqrt(24)" "=" "sqrt(3xx8) " "=" "sqrt(3xx2xx2^2)" "=" "2sqrt(3)sqrt(2)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting this all together:")#

#6sqrt(3)-5sqrt(3)+2sqrt(3)sqrt(2)#

#sqrt(3)+2sqrt(3)sqrt(2)#

#sqrt(3) (1+2sqrt(2))#