Square Root Of 1/2

How do u find the square root of 1/2 * (square root of 8 + square root of 2)?

Expert Answers
hala718 eNotes educator| Certified Educator

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

neela | Student

To find the  sqrt(1/2)*( sqrt8+sqrt2).

solution:

  sqrt(1/2) * (sqrt8+sqrt2) = sqrt((1/2)*8)+ sqrt((1/2)*2)

= sqrt4+sqrt1= 2+1 =3.