Indices & Surds Quiz

1. Simplify: 3² × 3⁴

1. 3⁶
2. 3⁸
3. 6⁶
4. 9⁶

2. Simplify: 5⁷ ÷ 5³

1. 1⁴
2. 25⁴
3. 5²¹
4. 5⁴

3. Simplify: (2³)⁴

1. 2¹²
2. 2⁷
3. 6⁴
4. 8⁴

4. What is 4^(1/2)?

1. 0.5
2. 16
3. 2
4. 8

5. What is 8^(2/3)?

1. 16
2. 2
3. 4
4. 64

6. What is 5⁻²?

1. −10
2. −25
3. 1/10
4. 1/25

7. What is a 'surd'?

1. A number raised to a negative power
2. An irrational root that cannot be simplified to a whole number or fraction
3. Any fraction
4. Any number involving π

8. Simplify: √50

1. 10√5
2. 25√2
3. 5
4. 5√2

9. Simplify: √12 + √3

1. √15
2. 2√3 + √3
3. 3√3
4. 4√3

10. Expand and simplify: (√3 + 1)(√3 − 1)

1. √3 − 1
2. 0
3. 3 + 1 = 4
4. 3 − 1 = 2

11. What is 'rationalising the denominator'?

1. Converting a surd to a decimal
2. Rewriting a fraction so the denominator contains no surds
3. Simplifying a fraction by cancelling common factors
4. Squaring both sides of an equation

12. Rationalise: 1/√5

1. √5/25
2. √5/5
3. 1/5
4. 5/√5

13. Simplify: 2√18 − √8

1. √10
2. 2√10
3. 4√10
4. 6√2 − 2√2 = 4√2

14. What is 27^(−1/3)?

1. −1/3
2. −3
3. 1/3
4. 3

15. Simplify: (√5)²

1. √25
2. 10
3. 25
4. 5

16. Which of these is equal to 16^(3/4)?

1. 12
2. 4
3. 64
4. 8

17. Rationalise the denominator: 6/(2+√2). Multiply by conjugate (2−√2).

1. 12−6√2
2. 3(2−√2)
3. 6(2−√2)/2
4. 6(2−√2)/4

18. Simplify: x⁵ × x⁻² / x

1. x²
2. x³
3. x⁴
4. x⁸

19. If 2ˣ = 32, what is x?

1. 16
2. 4
3. 5
4. 6

20. Expand: (3 + √2)²

1. 11
2. 11 + 6√2
3. 9 + 2
4. 9 + 6√2 + 2