Simplifying surds: Class 9 practice
√(ab) = √a × √b for positive a, b. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Perfect squares
- Prime factorisation
The idea behind simplifying surds
√(ab) = √a × √b for positive a, b. Take out the largest perfect-square factor: √72 = √(36 × 2) = 6√2. Only like surds (same number under the root) can be added.
Step-by-step method
- Find the largest square factor of the number.
- Write √n = √(square) × √(rest).
- Combine like surds by adding their coefficients.
Worked example 1 (Basic)
Simplify √45.
- 45 = 9 × 5
- √45 = 3√5
- Answer: 3√5
Worked example 2 (Standard)
Simplify √243.
- 243 = 81 × 3
- √243 = 9√3
- Answer: 9√3
Worked example 3 (Challenge)
Simplify √50 + √8.
- = 5√2 + 2√2
- = 7√2
- Answer: 7√2
Common mistakes and misconceptions
- √(a + b) = √a + √b
- Adding unlike surds
Practice questions
- (Basic) Simplify √75.
- (Basic) Simplify √27.
- (Standard) Simplify √384.
- (Standard) Simplify √294.
- (Challenge) Simplify √125 + √45.
- (Challenge) Simplify √150 + √150.
Answer key with full working
- Q1: 75 = 25 × 3 → √75 = 5√3 → Answer: 5√3
- Q2: 27 = 9 × 3 → √27 = 3√3 → Answer: 3√3
- Q3: 384 = 64 × 6 → √384 = 8√6 → Answer: 8√6
- Q4: 294 = 49 × 6 → √294 = 7√6 → Answer: 7√6
- Q5: = 5√5 + 3√5 → = 8√5 → Answer: 8√5
- Q6: = 5√6 + 5√6 → = 10√6 → Answer: 10√6
Syllabus note
This skill is listed under "Number Systems" for Class 9 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is simplifying surds in?
"Number Systems", Class 9 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.