Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144...
x², x⁴, x⁶, x⁸, x¹⁰... Exponents must be even.
√25 = 5 because 5² = 25
√36 = 6 because 6² = 36
√100 = 10
√49 = 7
√a⁶ = a³ because (a³)² = a⁶
√m¹⁰ = m⁵ because (m⁵)² = m¹⁰
√y¹⁰ = y⁵
√a² = a
Hint: Divide the exponent by 2.
In the expression √a, the √ is called the radical and a is called the radicand.
Simplify (Simplifying Perfect Squares):
1. 2
2. 4
3. -10
4. a⁴
5. w⁷
6. a⁵b⁵
7. 3y
8. -9m³
9. 7ab³
10. 11x²y³
Simplify (Simplifying Radicals that are not Perfect Squares):
1. √20 = √4 · √5 = 2√5
2. √27 = √9√3 = 3√3
3. √48 = √16√3 = 4√3
4. √45 = √9 · √5 = 3√5
5. √12 = √4 · √3 = 2√3
6. √50 = √25 · √2 = 5√2
7. √a⁵ = √a⁴ · √a = a²√a
8. √x⁹ = √x⁸ · √x = x⁴√x
9. √x³ = x√x
Simplify:
1. 3√2
2. 5√5
3. 6√2
4. 4√5
5. a²√a
6. b³√b
7. m⁵√m
8. 5y²√3y
9. 3a√3b
10. 4a²b²√2
11. 3a⁴
12. 3a³√5
13. 2a³b³√6
14. 2x⁵y⁴√3
15. -10√2
16. 4√6
17. 3x²y²√7
18. x²√6x
19. 10x²y²√x
20. 2a²b³c⁵√5ac
Parent Tip: Review the logic above to help your child master the concept of radical review worksheet answers.
