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y = x^(1/2) (NB power of '1/2' mean the 'square root'. Hence dy/dx = (1/2)x^(-1/2) or dy/dx = 1/ [2x^(1/2)]
By root, I think you mean square root. The square root of 2 is approx. 1.414. The square root of 9 = 3, so this goes exactly at 3 on the number line. Square root 2 will be less than 1/2 way between 1 and 2 on the number line.
A perfect square number is a number, whose square root is an integer. Examples are 1, 4, 9, 16, 25, .... The square roots of these numbers are {1,2,3,4,5,...} and {-1,-2,-3,-4,-5,...}
1 ft = 12 in 1 ft^2 = (12 in)^2 1 ft^2 = 144 in^2
1 is less than the square root of 2.