# Khan/khan-exercises

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randFromArray([30, 42, 66, 70, 105, 110, 154, 165, 210]) getPrimeFactorization(NUM).join("\\cdot")

Simplify \sqrt{NUM}.

NUM

NUM = FACTORS

NUM has no perfect-square factors, so \sqrt{NUM} is already the simplest form.

\sqrt{NUM} = 1\sqrt{NUM} or just \sqrt{NUM}.

randFromArray([9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225]) splitRadical(NUM) SPLIT[0] === 1 ? "" : SPLIT[0]

Simplify \sqrt{NUM}.

NUM

NUM = round(sqrt(NUM))^2

So, \sqrt{NUM} = \sqrt{SPLIT[0]^2} = SPLIT[0]

\sqrt{NUM} = SPLIT[0]\sqrt{1} or just SPLIT[0].

randFromArray([8, 12, 18, 20, 24, 27, 28, 32, 40, 44, 45, 48, 50, 54, 56, 60, 63, 72, 75, 80, 88, 90, 98, 99, 120, 125, 128, 140, 150, 160, 175, 180, 200, 216]) splitRadical(NUM) SPLIT[0] === 1 ? "" : SPLIT[0] SPLIT[1] === 1 ? "" : SPLIT[1]

Simplify \sqrt{NUM}.

NUM

The largest perfect square that divides NUM is COEFFICIENT * COEFFICIENT.

NUM = COEFFICIENT * COEFFICIENT \cdot RADICAL

\sqrt{NUM} = \sqrt{COEFFICIENT * COEFFICIENT \cdot RADICAL}

\sqrt{NUM} = \sqrt{COEFFICIENT * COEFFICIENT} \cdot \sqrt{RADICAL}

Thus, \sqrt{NUM} = COEFFICIENT\sqrt{RADICAL}.

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