# Concept derivation guides

299 concept teaching guides, separate from the 36,000 individual question derivations.

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Concept guide



## [Natural-number powers and principal square roots: computing powers by recursion and proving √(a²)=|a|](/en/derivations/derivation-mko-power-root-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-power-root)

Using only the recursive definition a^0=1, a^(n+1)=a^n·a, compute (−2)^n for n=0,1,2,3,4 and 0^0, 0^3; prove that a nonnegative square root is unique and that √(a²)=|a| for every real a; then find √49, √((−5)²) and the real solution set of y²=9, and explain why √(−4) is not defined in the reals.

Natural-number powers and principal square roots

derivation-mko-power-root-01





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