Adding numbers under the root sign H
"The Root Addition Error"
The Mistake in Action
Simplify $\sqrt{9 + 16}$
Wrong: $\sqrt{9 + 16} = \sqrt{9} + \sqrt{16} = 3 + 4 = 7$
Why It Happens
Students wrongly extend the rule $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ to addition.
The Fix
$\sqrt{a + b} \neq \sqrt{a} + \sqrt{b}$ — This is a critical rule!
The correct approach: $$\sqrt{9 + 16} = \sqrt{25} = 5$$
Quick check: $\sqrt{9} + \sqrt{16} = 3 + 4 = 7$, but $\sqrt{25} = 5 \neq 7$
What IS true:
- $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ ✓
- $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ ✓
- $\sqrt{a + b} = \sqrt{a} + \sqrt{b}$ ✗
Spot the Mistake
Can you identify where this student went wrong?
$\sqrt{9 + 16}$
$= \sqrt{9} + \sqrt{16}$
$= 7$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: