Add or subtract as indicated and simplify.
$6\sqrt[4]{3y}+2\sqrt[4]{3y}-5\sqrt[4]{3y}$

• A. $3\sqrt[4]{3y}$
• B. $5\sqrt[4]{3y}$
• C. $\sqrt[4]{3y}$
• D. $3\sqrt[4]{6y}$

Answer: (A)

Verified step by step guidance

1. Identify the like terms in the expression: \$6\sqrt[4]{3y} + 2\sqrt[4]{3y} - 5\sqrt[4]{3y}\(. Since all terms contain the same radical part \)\sqrt[4]{3y}$, they are like terms and can be combined by adding or subtracting their coefficients.
2. Add and subtract the coefficients of the like terms: \$6 + 2 - 5$. This will give you the combined coefficient for the radical expression.
3. Write the simplified expression by multiplying the combined coefficient by the common radical: \((6 + 2 - 5) \times \sqrt[4]{3y}\).
4. Simplify the arithmetic inside the parentheses to find the new coefficient, but do not calculate the final numeric value as per instructions.
5. Express the final simplified form as the product of the simplified coefficient and the fourth root of \$3y\(: \)\text{(simplified coefficient)} \sqrt[4]{3y}$.