Surds & Indices Questions and Answers
Practice ModeShowing 10 of 25 questions
Q1
Simplify: √50 + √18
Answer: Option A
Explanation: √50 = 5√2, √18 = 3√2, so 5√2 + 3√2 = 8√2
Q2
Simplify: (√3 + √2)(√3 - √2)
Answer: Option A
Explanation: Using formula (a+b)(a-b) = a² - b², we get (√3)² - (√2)² = 3 - 2 = 1
Q3
Find the value of 16^(3/4)
Answer: Option A
Explanation: 16^(3/4) = (2^4)^(3/4) = 2^(4 × 3/4) = 2^3 = 8
Q4
Simplify: √12 × √27
Answer: Option A
Explanation: √12 = 2√3, √27 = 3√3, so 2√3 × 3√3 = 6 × 3 = 18
Q5
If 2^x = 8, then find x
Answer: Option A
Explanation: 8 = 2^3, so 2^x = 2^3, therefore x = 3
Q6
Simplify: (√8 + √32)/√2
Answer: Option A
Explanation: √8 = 2√2, √32 = 4√2, so (2√2 + 4√2)/√2 = 6√2/√2 = 6
Q7
Find the value of 125^(-2/3)
Answer: Option A
Explanation: 125^(-2/3) = (5^3)^(-2/3) = 5^(-2) = 1/25
Q8
Simplify: √75 - √48
Answer: Option A
Explanation: √75 = 5√3, √48 = 4√3, so 5√3 - 4√3 = √3
Q9
If 3^(x+1) = 81, find x
Answer: Option A
Explanation: 81 = 3^4, so 3^(x+1) = 3^4, therefore x+1 = 4, x = 3
Q10
Simplify: (2√3 + 3√2)^2 - (2√3 - 3√2)^2
Answer: Option A
Explanation: Using a² - b² = (a+b)(a-b), we get (4√3)(6√2) = 24√6