Grade 11 · Theory
Simplifying surds
Exponents and surds · about 3 min
Visual overview: Simplifying surds1 MIN READ
2 study sections · pause after each one and recall the key ideaA surd is an exact irrational root. Simplifying keeps answers exact and is expected in the exam.
Key points- √(ab) = √a × √b — extract perfect squares: √50 = √25 × √2 = 5√2.
- Only LIKE surds can be added or subtracted: 3√2 + 5√2 = 8√2.
- Rationalise a denominator by multiplying top and bottom by the surd (or its conjugate).
- Leave answers in surd form unless a decimal is requested.
- Surd — an irrational root left in exact form.
- Conjugate — (a + √b) and (a − √b).
EXAM TIP
never write √2 + √3 = √5 — you cannot add surds inside the root.