How do you simplify #sqrt(1/8)#?

2 Answers
Mar 28, 2018

Answer:

#sqrt2/4#

Explanation:

Looking at the given expression:
#sqrt(1/8)#

By: #sqrt(a/b)= sqrta/sqrtb#

#sqrt(1/8)=sqrt1/sqrt8#

Which is:

#sqrt1/sqrt8= 1/sqrt8#

Simplify:
#1/sqrt8=1/sqrt(2*4)#

#1/sqrt(2*4)= 1/(2sqrt2)#

Rationalize the denominator:
#1/(2sqrt2)*sqrt2/sqrt2= sqrt2/4#

Mar 28, 2018

Answer:

#sqrt(1/8)=color(blue)(sqrt2/4#

Explanation:

Simplify:

#sqrt(1/8)#

Apply square root rule: #sqrt(a/b)=sqrta/sqrtb; b!=0#

#sqrt1/sqrt8#

Simplify #sqrt1# to #1#.

#1/sqrt8#

Rationalize the denominator.

#1/sqrt8xxsqrt8/sqrt8#

#sqrt8/(sqrt8sqrt8)#

Apply square root rule: #sqrtasqrta=a#

#sqrt8/8#

Prime factorize #sqrt8#.

#sqrt(2xx2xx2)/8=#

#sqrt(2^2xx2)/8#

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

#(color(red)cancel(color(black)(2))^1sqrt2)/color(red)cancel(color(black)(8))^4#

Simplify.

#sqrt2/4#