Simplify the following:
2 sqrt(2)×2 sqrt(2)
2 sqrt(2)×2 sqrt(2) = 2^(1+1/2+1+1/2):
2^(1+1/2+1+1/2)
Put 1+1/2+1+1/2 over the common denominator 2. 1+1/2+1+1/2 = 2/2+1/2+2/2+1/2:
2^2/2+1/2+2/2+1/2
2/2+1/2+2/2+1/2 = (2+1+2+1)/2:
2^(2+1+2+1)/2
2+1+2+1 = 6:
2^(6/2)
The gcd of 6 and 2 is 2, so 6/2 = (2×3)/(2×1) = 2/2×3 = 3:
2^3
2^3 = 2×2^2:
2×2^2
2^2 = 4:
2×4
2×4 = 8:
Answer: | 8
