Maths-
General
Easy

Question

Factor the given radicand using the product property of square roots. √200

hintHint:

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- 10√2


    Step-by-step solution:-
    Given expression = √200
    ∴ Given expression = √2 × 2 × 2 × 5 × 5 …................................. (Factorising the given radicand)
    ∴ Given expression = √(2 × 2) × √(5 × 5)  ×√2 …........................ [Product property of radicals i.e. √m × √n = √(mn)]
    ∴ Given expression = √(2)2 × √(5)2 × √2
    ∴ Given expression = (2)2/2 × (5)2/2 × √2 .................................... [Power rule- m√(bn) = b n/m]
    ∴ Given expression = (2)1 × (5)1 × √2
    ∴ Given expression = 2 × 5 × √2
    ∴ Given expression = 10√2
    Final Answer:-
    ∴ The given radicand can be factorised using product property as- 10√2

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