Rewrite expressions with radicals and rational exponents using exponent properties.
Simplify a radical by factoring out a perfect square or perfect cube
Problem
Simplify \(\sqrt{72}\) by factoring \(72\) into its greatest perfect-square factor times the remaining radicand.
Big Picture
What this problem is really about
Simplifying a radical starts with the greatest perfect-power factor that matches its root index. We’ll factor the radicand, split the root across the product, evaluate the extractable square, leave the square-free remainder inside, and square the simplified expression to verify it.
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