How do you simplify #sqrt(84)#?
√84=√4*21 = 2√21
Always check if the number inside the root can be broken down into a perfect square which is also must be a factor. then write as √4*21 then take out the 4. when it is taken out '4', factors out and becomes 2 as in 2√21. this can be done until no perfect squares are left inside the root.
# 2sqrt21 #
To simplify a radical write in the form
# asqrtb #
To obtain this form : consider the factors of 84 ,finding if possible one which is a perfect square.
in this case: 84 = 4
# xx 21 and so sqrt84 = sqrt(4 xx 21) #
#sqrt(ab) = sqrta xx sqrtb rArr sqrt(4 xx 21) =sqrt4 xx sqrt21#
21 cannot be simplified any further as it's factors are all prime and so
#sqrt84 = sqrt4 xx sqrt21 = 2sqrt21 #