⚠️ Not fully simplifying a surd H

"The Partial Simplify"

Number & Proportion

The Mistake in Action

Simplify $\sqrt{72}$

Wrong: $\sqrt{72} = \sqrt{4 \times 18} = 2\sqrt{18}$ ✓ Done

🧠 Why It Happens

Students find one square factor but don't check if the remaining surd can be simplified further.

The Fix

Always check if your answer can be simplified further!

$\sqrt{72} = \sqrt{4 \times 18} = 2\sqrt{18}$

But $\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$

So: $\sqrt{72} = 2 \times 3\sqrt{2} = 6\sqrt{2}$

Better method: Find the largest square factor. $72 = 36 \times 2$ $\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}$

🔍 Spot the Mistake

Can you identify where this student went wrong?

$\sqrt{72} = 2\sqrt{18}$

Click on the line that contains the error.

📚 Related Topics

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