Question

which is equivalent to \\((3\sqrt{12x^5})(4\sqrt{12x^3})\\)?

a. \\(144x^8\\)
b. \\(144x^4\\)
c. \\(24x^8\\)
d. \\(12x^4\\)

Explanation:

Multiply the coefficients and the radicals

$$ (3\sqrt{12x^5})(4\sqrt{12x^3}) = (3 \cdot 4) \sqrt{(12x^5)(12x^3)} $$

Simplify the product inside the radical

$$ 12 \sqrt{144x^8} $$

Evaluate the square root

$$ 12 \cdot 12x^4 = 144x^4 $$

Answer:

• A. \(144x^8\)
• B. \(144x^4\) (Correct answer)
• C. \(24x^8\)
• D. \(12x^4\)