How do you simplify #sqrt 8 /( 2 sqrt3)#?

3 Answers
Feb 28, 2016

Answer:

#(sqrt8)/(2sqrt 3)=color(blue)((sqrt 6)/3)#

Explanation:

#(sqrt 8)/(2sqrt 3)#

Simplify #sqrt 8#.

#sqrt 8=sqrt(2xx2xx2)=sqrt(2^2xx 2)=2sqrt2#

Rewrite the fraction.

#(2sqrt2)/(2sqrt 3)#

Rationalize the denominator by multiplying the numerator and denominator by #sqrt 3#.

#(2sqrt2)/(2sqrt 3)xx(sqrt3)/(sqrt 3)#

Simplify.

#(2sqrt2sqrt3)/(2xx3)#

Simplify.

#(2sqrt6)/(2xx3)#

Simplify.

#(cancel2sqrt6)/(cancel2xx3)#

Simplify.

#(sqrt 6)/3#

Feb 28, 2016

Answer:

#sqrt (2/3)#

Explanation:

#8=2^3#
#sqrt (8) = 2^(3/2)#

Therefore we have

#(2^(3/2).2^(-1))/sqrt (3)#

Add the exponent coefficients for 2

#(2^(1/2))/sqrt (3)#

Same as #sqrt(2/3)#

Feb 28, 2016

Answer:

#sqrt(2/3)#

Explanation:

#sqrt8/(2sqrt3)#

We could see that

#sqrt8=sqrt(4*2)#

So

#=sqrt(4*2)/(2sqrt3_#

#=(cancel2sqrt2)/(cancel2sqrt3)#

#=sqrt2/sqrt3=sqrt(2/3)#

But wait ! We could not have irrational numbers in the denominator.

So,rationalize the denominator by multiplying with #sqrt3/sqrt3#

#sqrt2/sqrt3*sqrt3/sqrt3#

#=sqrt6/3#