How do you rationalize #sqrt(14/x)#?

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Answer 1 · 2018-05-29T17:15:55

#(sqrt(14x))/x#

#x!=0#

#=sqrt(14/x)#

Assume #x!=0#

#=sqrt14/sqrtx#

#=sqrt14/sqrtx*sqrtx/sqrtx#

#=(sqrt(14x))/x#

Answer 2 · 2018-05-29T17:16:33

See a solution process below:

First, multiply the term under the radical by the appropriate form of #1#:

#sqrt(x/x * 14/x) =>#

#sqrt((14x)/x^2)#

Next, use this rule for radicals to simplify the expression:

#sqrt(color(red)(a)/color(blue)(b)) = sqrt(color(red)(a))/sqrt(color(blue)(b))#

#sqrt(color(red)(14x)/color(blue)(x^2)) =>#

#sqrt(color(red)(14x))/sqrt(color(blue)(x^2)) =>#

#sqrt(color(red)(14x))/color(blue)(x)#