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In a recent Note [1] Michael D. Hirschhorn presented high order algorithms for calculating numerically square roots and cube roots. In particular, he obtained the method
(1)
with 
, where the convergence is of tenth order:
We recall his idea in the case of an arbitrary square root 
with a > 0. Let p ⩾ 2 be a fixed integer. Our starting point is the relation
Choose
