How do you simplify #sqrt12- sqrt 50+ sqrt 72#?

1 Answer
Jul 16, 2017

Answer:

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

Explanation:

You are looking for squared numbers that you can 'take outside' the root and any repeated values that you can combine.

Notice that all the numbers are even so lets play with that to start with.

#sqrt(2xx6)-sqrt(2xx25)+sqrt(2xx36)#

#sqrt(2xx2xx3)-sqrt(2xx5^2)+sqrt(2xx6^2)#

#sqrt(2^2xx3)-sqrt(2xx5^2)+sqrt(2xx6^2)#

'Take out' the squared values

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

Note that 6 of something - 5 of something leaves 1 of something

#2sqrt(3)+[color(white)(.)6sqrt(2)-5sqrt(2)color(white)(.)]#

#2sqrt(3)+ sqrt(2)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check:

#sqrt(12)-sqrt(50)+sqrt(72)~~ 4.8783...#

#2sqrt(3)+ sqrt(2)~~ 4.8783....#