Dumela! Prof. Kitso here with this week’s trap — a small habit that quietly costs real marks.
√50 = √(25 × 2) = 25√2 ✗
√50 = √25 × √2 = 5√2 ✓
√50 = √25 × √2 = 5√2 ✓
Why your brain does it: You correctly spot the square factor 25, then walk it out of the root unchanged. But leaving a square root means taking the root.
The fix: Split into the biggest square factor times the rest: √50 = √25 · √2. Then root what you can: √25 = 5. Answer 5√2. Sanity check: 5√2 ≈ 7.07, and 7.07² ≈ 50 ✓. 25√2 ≈ 35 — nowhere near.
Remember it as: A square factor comes out as its ROOT. 25 goes in, 5 comes out.
Remember it as: A square factor comes out as its ROOT. 25 goes in, 5 comes out.
Where this bites in real life: Every diagonal you ever calculate — a TV screen, a roof brace, a football pitch — lands on a surd. Simplifying makes it a number you can actually use.
Your turn — 60 seconds
1. √18
3√2
2. √75
5√3
3. √8 + √2
3√2 — simplify first, then add.
All three right? This trap is finished with you. Missed one? Unit 19 — Root and Branch in the Algebra Revision course rebuilds it from scratch with sixty practice questions.
Not sure where your maths actually stands? The free placement quiz takes 40 minutes and names the exact unit you should start with.
Take the free placement quiz
Prof. Kitso
Stadira School Programmes · a new trap every week
Stadira School Programmes · a new trap every week
