How do you simplify the expression #2sqrt(1/2)+2sqrt2-sqrt8#?

1 Answer
May 7, 2017

Answer:

#2sqrt(1/2)+2sqrt2-sqrt8=color(blue)(sqrt2#

Explanation:

Simplify.

#2sqrt(1/2)+2sqrt2-sqrt8#

In order to add or subtract numbers with square roots, the square roots must be the same.

Simplify #sqrt8# by prime factorization.

#2sqrt(1/2)+2sqrt2-sqrt(2xx2xx2)#

#2sqrt(1/2)+2sqrt2-sqrt(2^2xx2)#

#2sqrt(1/2)+2sqrt2-2sqrt2#

Simplify #sqrt(1/2)# to #(sqrt1)/(sqrt2)#.

#2xx(sqrt1)/(sqrt2)+2sqrt2-2sqrt2#

Simplify #sqrt1# to #1#.

#2xx1/(sqrt2)+2sqrt2-2sqrt2#

Rationalize the denominator by multiplying the numerator and denominator by #color(red)(sqrt2#.

#2xx1/(sqrt2)xxcolor(red)(sqrt2)/color(red)(sqrt2)+2sqrt2-2sqrt2#

Simplify.

#(2xxsqrt2)/(sqrt2xxsqrt2)+2sqrt2-2sqrt2#

Simplify.

#(2sqrt2)/2+2sqrt2-2sqrt2#

Cancel the #2/2#.

#(color(red)cancel(color(black)(2))sqrt2)/color(red)cancel(color(black)(2))+2sqrt2-2sqrt2#

#sqrt2+2sqrt2-2sqrt2#

Simplify.

#3sqrt2-2sqrt2#

Answer.

#sqrt2#