sqrt(1/2)* (sqr8+sqrt2)

Let us first simplify:

sqrt(8)= sqrt(2*2*2)= sqrt(2*2^2)=sqrt2*sqrt2^2=2sqrt(2)

Now substitute:

sqrt(1/2)*(2sqrt2+sqrt2)

Factorize sqrt(2):

sqrt(1/2)*sqrt(2)(2+1)

= [1/sqrt(2)]*sqrt(2)*3

= [sqrt(2)/sqrt(2)]*3 =3

sqrt(1/2)* (sqr8+sqrt2)

Let us first simplify:

sqrt(8)= sqrt(2*2*2)= sqrt(2*2^2)=sqrt2*sqrt2^2=2sqrt(2)

Now substitute:

sqrt(1/2)*(2sqrt2+sqrt2)

Factorize sqrt(2):

sqrt(1/2)*sqrt(2)(2+1)

= [1/sqrt(2)]*sqrt(2)*3

= [sqrt(2)/sqrt(2)]*3 =3