Rewrite expression to remove perfect square factors other than 1 in radicand. √100x⁸

The correct answer is: The given expression can be written as 10x4 after removing all perfect square factors other than 1

Step-by-step solution:-
Given expression = √100x8
∴ Given expression = √(2 × 2 × 5 × 5 × x² ×x² × x² × x²) ….......................... (Factorizing the term inside the radical)
∴ Given expression = √(2 × 2) × √(5× 5)× √x² × √x² × √x² × √x² …..................... [Product property- √m × √n = √(mn)]
∴ Given expression = √(2)² × √(5)² × √(x)² × √(x)² × √(x)² ×√(x)²
∴ Given expression = (2)^2/2 × (5)^2/2 × (x)^2/2 × (x)^2/2 × (x)^2/2 × (x)^2/2 ............................ [Power rule- ^m√(bⁿ) = b ^n/m]
∴ Given expression = (2)¹× (5)¹× (x)¹× (x)¹ × (x)¹ × (x)¹
∴ Given expression = 2 × 5 × x × x × x × x
∴ Given expression = 10 × x⁴
∴ Given expression = 10x⁴
Final Answer:-
∴ The given expression can be written as 10x⁴ after removing all perfect square factors other than 1.