Surds & Indices Questions and Answers
Practice ModeShowing 10 of 25 questions
Q11
Find the value of 4^(3/2)
Answer: Option A
Explanation: 4^(3/2) = (2^2)^(3/2) = 2^3 = 8
Q12
Simplify: √128 - √50
Answer: Option A
Explanation: √128 = 8√2, √50 = 5√2, so 8√2 - 5√2 = 3√2
Q13
If 5^x = 1/125, find x
Answer: Option A
Explanation: 1/125 = 5^(-3), so 5^x = 5^(-3), therefore x = -3
Q14
Simplify: (√12 + √27)^2
Answer: Option A
Explanation: √12 = 2√3, √27 = 3√3, sum = 5√3, square = (5√3)^2 = 25 × 3 = 75
Q15
Find the value of 8^(2/3)
Answer: Option A
Explanation: 8^(2/3) = (2^3)^(2/3) = 2^2 = 4
Q16
Simplify: √45 + √20
Answer: Option A
Explanation: √45 = 3√5, √20 = 2√5, so 3√5 + 2√5 = 5√5
Q17
If 4^(x-1) = 64, find x
Answer: Option A
Explanation: 64 = 4^3, so 4^(x-1) = 4^3, therefore x-1 = 3, x = 4
Q18
Simplify: (√18 × √8)/√36
Answer: Option A
Explanation: √18 = 3√2, √8 = 2√2, product = 6×2 = 12, √36 = 6, so 12/6 = 2
Q19
Find the value of 27^(-1/3)
Answer: Option A
Explanation: 27^(-1/3) = (3^3)^(-1/3) = 3^(-1) = 1/3
Q20
Simplify: √200 - √72
Answer: Option A
Explanation: √200 = 10√2, √72 = 6√2, so 10√2 - 6√2 = 4√2