Question

"Write a product of two square roots so that the answer, when simplified, is (12x^3y^2). Show how your product simplifies to give the correct answer.

a) (2x^2 √{6xy})
b) (2x √{3xy^2})
c) (2x^2 √{3y^2})
d) (4x^2 √{3y})"

Answer 1

The product of two square roots that simplifies to (12x^3y^2) is (2x^2 * √(6xy) * √(y^2)), which further simplifies to (2x^2 √(6xy^3)).Correct option is b.

Step-by-step explanation:

To find the product of two square roots that simplifies to (12x^3y^2), we can use the property √a * √b = √(ab). In this case, we want to find the square root of two expressions containing variables.

First, we can simplify (12x^3) as (2x^2) * (6x), and simplifying (y^2) as √y * √y. Therefore, the product of two square roots that simplifies to (12x^3y^2) is (2x^2 √(6xy) * √(y^2)). This simplifies to (2x^2 √(6xy) * y), which can be further simplified to (2x^2 √(6xy^3)).