Maths-
General
Easy
Question
Factor the given radicand using the product property of square roots. √40x4
Hint:
A radical expression refers to an expression containing a radical (√) symbol, commonly called as a root symbol.
A radicand refers to the number that is preceded by a radical sign.
The correct answer is: The given radicand can be factorised using product property as- 2x2√10
Step-by-step solution:-
Given expression = √40x4
∴ Given expression = √2 × 2 × 2 × 5 × x2 x2 …................................. (Factorising the given radicand)
∴ Given expression = √(2 × 2) × √(2 ×5) × √(x2 x2) …........................ [Product property of radicals i.e. √m × √n = √(mn)]
∴ Given expression = √(2)2 × √(x2)2 × √2 × 5
∴ Given expression = (2)2/2 × (x2)2/2 × √2 × 5 .................................... [Power rule- m√(bn) = b n/m]
∴ Given expression = (2)1 × (x2)1 × √2 × 5
∴ Given expression = 2 × x2 × √2 × 5
∴ Given expression = 2x2√10
Final Answer:-
∴ The given radicand can be factorised using product property as- 2x2√10
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