WORKSHEET ON Nth ROOTS

Problem 1 :

Simplify :

⁴√(x⁴)

Problem 2 :

Simplify :

⁵√(x¹⁰)

Problem 3 :

Simplify :

³√(x⁴)

Problem 4 :

Simplify :

⁴√(81x⁸y⁴)

Problem 5 :

Simplify :

√32 + √200

Problem 6 :

Simplify the following expression, if b > o.

√(25b) - √(b³)

Answers

1. Answer :

⁴√(x⁴) = x

2. Answer :

⁵√(x¹⁰) = ⁵√[(x²)⁵]

= x²

3. Answer :

³√(x⁴) = ³√(x³x)

= ³√(x³) ⋅ √x

= ³√(x³) ⋅ ³√x

= x(³√x)

4. Answer :

⁴√(81x⁸y⁴) = ⁴√81 ⋅ ⁴√x⁸ ⋅ ⁴√y⁴

= ⁴√(3⁴) ⋅ ⁴√(x²)⁴ ⋅ ⁴√y⁴

= 3x² ⋅ |y|

= 3x²y

5. Answer :

√32 + √200 = √(16 ⋅ 2) + √(100 ⋅ 2)

= √16 ⋅ √2 + √100 ⋅ √2

= 4√2 + 10√2

= (4 + 10)√2

= 14√2

6. Answer :

√(25b) - √(b³) = √25√b - √(b² ⋅ b)

= √25√b - √(b²)√b

= √25√b - √(b²)√b

= 5√b - b√b

= (5 - b)√b

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