Rewrite expression to remove perfect square factors other than 1 in radicand. 4x√1/4x6

The correct answer is: The given expression can be written as 2x4 after removing all perfect square factors other than 1

Hint:-
A radical expression refers to an expression containing a radical (√) symbol, commonly called as a root symbol.
A perfect square refers to a number that can be expressed as the product of an integer by itself.
We will simplify the given expressions, removing all the perfect square factors from under the radical sign.
"Step-by-step solution:-
Given expression = 4x × √(1/4x6)
∴ Given expression = 4x × √(1/2 × 1/2 × x × x × x × x × x × x) ….......................... (Factorizing the term inside the radical)
∴ Given expression = 4x × √(1/2 × 1/2) × √(x × x) × √(x × x) × √(x × x) …..................... [Product property- √m ×√n = √(mn)]
∴ Given expression = 4x × √(1/2)2 ×√(x)2 ×√(x)2 × √(x)2
∴ Given expression = 4x × (1/2)2/2 × (x)2/2 × (x)2/2 × (x)2/2 ............................ [Power rule- m√(bn) = b n/m]
∴ Given expression = 4x × (1/2)1 × (x)1 × (x)1 × (x)1
∴ Given expression = 4x × 1/2 × x × x × x
∴ Given expression = 4 × 1/2 × x × x × x × x
∴ Given expression = 2x4
Final Answer:-
∴ The given expression can be written as 2x4 after removing all perfect square factors other than 1.