Question

"Write a product of two square roots so that the answer, when simplified, is (12x^3y^2).

A. (2√{3x} ×6x^{{3}{2}} ×√{y^2})

B. (2√{3x} ×2x^{{3}{2}} ×3y)

C. (4√{3x} ×3x^{{3}{2}} ×√{y^2})

D. (6√{2x} ×2x^{{3}{2}} ×√{y})"

Answer 1

The correct answer is A. (2√{3x} ×6x^{{3}{2}} ×√{y^2}). To simplify the answer, we need to use the rules of multiplying square roots.

Step-by-step explanation:

The correct answer is A. (2√{3x} ×6x^{{3}{2}} ×√{y^2}).

To simplify the answer, we need to use the rules of multiplying square roots.

Step 1: Simplify the square roots. √{3x} × √{y^2} = √{(3x)(y^2)} = √{3xy^2}.

Step 2: Multiply the coefficients. 2 × 6 = 12.

Step 3: Multiply the variables. x^{{3}{2}} × x^{{1}{2}} × y^2 = x^{{3+1}{2}} × y^2 = x^{{4}{2}} × y^2 = x^2y^2.

Putting it all together, we have (2√{3x} ×6x^{{3}{2}} ×√{y^2}) = (12x^2y^2), which matches the given answer (12x^3y^2).