Because the square root of 32 is an irrational number
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32 is 2 x2x2x2x2 = 4 x 4 x 2
Hence sqrt(32) = sqrt(4 x 4 x2)
THe RHS can be rewritten as sqrt(4) X sqrt(4) x sqrt(2)
The sqrt (4) = 2
Hence
2 x 2 xsqrt(2) = 4 sqrt(2) = 32
Square root of 4 is 2 and so 2 times 16 = 32
√3 / √(-32) = √(-3 / 32) = √(-3 / 2) / 4 = i√(3/2) / 4
√32 = 4√2 ≈ 5.657
sqrt(32) = 4 sqrt(2) = 5.6569 (rounded)
√32 = √(16 x 2)= √16 x √2= 4 √2