Write an expression for each product without perfect square factors in the radicand.  × √21x³ × 4√7x²

The correct answer is: The given expressions can be written using without a perfect square in the radicand as- 14x2√3x

Step-by-step solution:-
Given expression =  × √21x³ × 4√7x²
∴ Given expression = × √(21 × x × x × x) × 4 × √(7 × x × x) …................................ (Factorising the given radicand)
∴ Given expression = √21 × √(x × x) × √x × 4 × √7 × √(x × x) …........................ [Product property of radicals i.e. √m × √n = √(mⁿ)]
∴ Given expression =  × √21 × √x² × √x × 4 × √7 × √x²
∴ Given expression =  × 4 × √21 × √7 × √x × (x)^2/2 × (x)^2/2 .................................... [Power rule- m√(bⁿ) = b ^n/m]
∴ Given expression = 2 × √(21 × 7 × x) × x¹ × x¹
∴ Given expression = 2 × √147x × x²
∴ Given expression = 2 × √(7 × 7 × 3 × x) × x² ….......................................................... (Factorising the given radicand)
∴ Given expression = 2 × x² × √(7 × 7) ×√(3 × x) ......................................................... [Product           property  of radicals i.e. √m × √n = √(mn)]
∴ Given expression = 2 × x² × 7 × √3x
∴ Given expression = 14x²√3x
Final Answer:-
∴ The given expressions can be written using without a perfect square in the radicand as- 14x²√3x.