How do you simplify #sqrt28/sqrt7#?

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Answer 1 · 2018-03-18T05:42:53

#2#

Given: #sqrt(28)/sqrt(7)#

We got:

#sqrt(28)=sqrt(4*7)#

#=sqrt(4)*sqrt(7)#

#=2*sqrt(7)#

#2sqrt(7)#

So, the expression becomes:

#(2sqrt(7))/sqrt(7)#

#=(2color(red)cancelcolor(black)(sqrt(7)))/color(red)cancelcolor(black)(sqrt(7))#

#=2#

Answer 2 · 2018-03-18T06:02:40

#(sqrt28)/(sqrt7)=color(blue)2#

Simplify:

#(sqrt28)/(sqrt7)#

Rationalize the denominator by multiplying the numerator and denominator by #sqrt7#.

#(sqrt28sqrt7)/(sqrt7sqrt7)#

Apply rule: #sqrtasqrta=a#

#(sqrt28sqrt7)/7#

Prime factorize #sqrt28#.

#(sqrt(2^2*7)sqrt7)/7#

Apply rule: #sqrt(a^2)=a#

#(2sqrt7sqrt7)/7#

Apply rule: #sqrtasqrta=a#

#(2xx7)/7#

Cancel #7#.

#(2xxcolor(red)cancel(color(black)(7))^1)/color(red)cancel(color(black)(7))^1#

Simplify.

#2#