How do you simplify #sqrt(50) - sqrt(18)?#

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Answer 1 · 2018-06-11T19:21:00

#2sqrt2#

The key realization here is that we can leverage the radical property

#sqrt(ab)=sqrtasqrtb#

Thus, we can rewrite #color(blue)(sqrt50)-color(red)(sqrt18)# as

#color(blue)(sqrt(25*2))-color(red)(sqrt(9*2))#

which simplifies to

#5sqrt2-3sqrt2#

Factoring out a #sqrt2#, we get

#sqrt2(5-3)#

Which simplifies to

#2sqrt2#

Hope this helps!