Quadratic Surd
Multiple Choice Questions (MCQ)
1. Which of the following is a uadratic surd?
A. 4
B. √9
C. √5
D. 25
Answer: C. √5
2. Simplify: √72
A. 4√3
B. 6√2
C. 5√2
D. 2√6
Answer: B. 6√2
3. What is the result of 3√2 + 5√2 − 2√3?
A. 8√2
B. 8√2 − 2√3
C. 8√5
D. 10√2 − 2√3
Answer: B. 8√2 − 2√3
4. Multiply: √2 × √8
A.√16
B. 8
C. 4
D. 2√4
Answer: C. 4
5. What is the rationalised form of 5 / √2?
A. 5/√2
B. √2 / 5
C. 5√2 / 2
D. 2√5 / 2
Answer: C. 5√2 / 2
Short Answer Questions (SAQ)
1. Define a uadratic surd.
Answer: A uadratic surd is an irrational number in the form of √a, where a is a positive number that is not a perfect suare.
2. Simplify: √50
Answer: √50 = √(25 × 2) = 5√2
3. Can 2√3 and 5√2 be directly added? Why or why not?
Answer: No, because they are unlike surds (different radical parts).
Long Answer Questions (LAQ)
1.Rationalise the denominator of: 3 / (2 + √3)
Answer: Multiply numerator and denominator by the conjugate (2 − √3):
32 + 3 × 2 – 32 – 3 = 3 (2 – 3) (2 – 3) (2 – 3)
=3 (2 – 3)4 – 3 = 3 (2 – 3)1 = 6−33
Final Answer: 6 − 3√3
2.Solve the euation: x² − 2x − 1 = 0 using the uadratic formula.
Answer: Given euation: x² − 2x − 1 = 0
Use uadratic formula: x = -(-2) (-2)2– 4(1) (-1) 2(1) = 2 4 + 42 = 2 82
= 2 2 22 = 1 ± √2
Final Answer: x = 1 + √2 or x = 1 − √2