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
