20 essential questions across core units — attempt each one, then check your understanding.
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Radicals★ Easy
Simplify: \(\sqrt{72}\)
🔑
Memory Point
FACTOR OUT PERFECT SQUARES: √(a·b) = √a · √b Find the largest perfect square that divides in.
Worked Example
\(\sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}\)
Same idea: break 72 into a perfect square × something.
💡 Explanation
\(\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36}\cdot\sqrt{2} = 6\sqrt{2}\).
The largest perfect square factor of 72 is 36 (not 4 or 9). Always find the largest perfect square to simplify fully in one step.