Verified answer

√200 - √32

√(100*2) - √(16*2)

10√2 - 4√2

6√2

sqrt(200) - sqrt(32)

= sqrt(100 * 2) - sqrt(16 * 2)

= 10sqrt(2) - 4sqrt(2)

= 6sqrt(2)

sqrt(200) = sqrt(10*2) = 10*sqrt(2)

sqrt(32) = sqrt(16*2) = sqrt(16)*sqrt(2) = 4*sqrt(2)

10*sqrt(2)-4*sqrt(2)= (10-4)*sqrt(2) = 6*sqrt(2)

root200 can be written root(2x100)=10root2

root32 can be written root (2x16) = 4root2

root200 - root32 = 10root2 - 4root2 = 6root2