Find the value of y if `(root(4)(y^8) )= 225`

Options

A. 10
B. 12
C. 15
D. 18

Answer

To solve the equation \( \sqrt[4]{y^8} = 225 \), we will follow these steps:

### Step 1: Rewrite the equation using exponent notation
The fourth root can be expressed as an exponent of \( \frac{1}{4} \). Therefore, we can rewrite the equation as:
\[ y^{8 \cdot \frac{1}{4}} = 225 \]

### Step 2: Simplify the exponent
Now simplify the exponent:
\[ y^{2} = 225 \]

### Step 3: Solve for \( y \)
To find \( y \), we take the square root of both sides:
\[ y = \sqrt{225} \]

### Step 4: Calculate the square root
Now, calculate the square root:
\[ y = 15 \]

### Conclusion
Thus, the value of \( y \) is:
\[ \boxed{15} \]

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