How do you simplify #4 *sqrt(3/4)#?

4 Answers
Jul 10, 2018

Answer:

#color(crimson)( => 2 sqrt 3#

Explanation:

#4 * sqrt(3/4)#

#=> (sqrt 4)^2 * sqrt 3 / sqrt 4#

#=> sqrt 4 * cancel (sqrt 4) * sqrt 3 / cancel sqrt 4#

#=> sqrt 4 * sqrt 3#

#color(crimson)( => 2 sqrt 3#

Jul 10, 2018

Answer:

#2sqrt3#

Explanation:

#4 cdot sqrt(3/4)#

#4 cdot sqrt3/sqrt4#

#4 cdot sqrt3/sqrt4 xx sqrt4/sqrt4#

#4 cdot (sqrt3 xx sqrt4)/(sqrt4 xx sqrt4)#

#4 cdot sqrt12/4#

#cancel4 cdot sqrt12/cancel4#

#sqrt12#

#sqrt(3 xx 4)#

#sqrt3 xx sqrt4#

#sqrt3 xx 2#

#2sqrt3#

Jul 10, 2018

Answer:

#color(blue)(=> 2 sqrt3#

Explanation:

#4 * sqrt (3/4)#

#=> 4 * sqrt 3 / sqrt 4#

#=>cancel(4)^color(red)(2) * sqrt 3 / cancel2#

#color(blue)(=> 2 sqrt3#

Jul 10, 2018

Answer:

#2sqrt3#

Explanation:

The key realization is that we can rewrite #sqrt(3/4)# as #sqrt3/sqrt4#. We now have

#4*sqrt3/sqrt4#

This simplifies to

#4*sqrt3/2#

Cancelling out common factors

#cancel(4)^2*sqrt3/cancel2#

#=>2sqrt3#

Hope this helps!