Final Answer:
B) √bya by applying the rule of splitting the square root of a product into the square roots of its factors, option B correctly represents the square root of ab.
Explanation:
The square root of ab is represented as √(ab), which can be expressed as √(a) * √(b). Hence, the square root of ab is the square root of a multiplied by the square root of b, represented as √a * √b. In the given options, √bya represents the square root of b multiplied by y and then by a, equivalent to √(b) * √(y) * √(a), which aligns with the mathematical principle of the square root of a product being the product of the square roots of individual factors. Therefore, the correct answer is B) √bya.
The square root (√) of a product (√(ab)) is calculated by breaking down the product into its prime factors. This property allows us to split the square root of a product into the square roots of its individual factors. Here, ab can be expressed as a * b, and the square root of ab (√(ab)) can be simplified to √(a) * √(b).
In the provided options, option B (√bya) aligns with this concept as it represents the square root of b multiplied by y and then by a, which essentially denotes the square roots of individual factors multiplied together: √(b) * √(y) * √(a).
Therefore, by applying the rule of splitting the square root of a product into the square roots of its factors, option B correctly represents the square root of ab.