`sqrt(225)+root(3)(1/64)=`_____

Options

A. `15 1/4`
B. `15 1/8`
C. `15 1/2`
D. `15 1/16`

Answer

To solve the expression \( \sqrt{225} + \sqrt[3]{\frac{1}{64}} \), we will break it down step by step.

### Step 1: Calculate \( \sqrt{225} \)
To find \( \sqrt{225} \), we can recognize that \( 225 \) is a perfect square:
\[ \sqrt{225} = 15 \]

### Step 2: Calculate \( \sqrt[3]{\frac{1}{64}} \)
Next, we need to find the cube root of \( \frac{1}{64} \). We can rewrite \( \frac{1}{64} \) as \( 64^{-1} \) or \( 64^{-\frac{1}{3}} \). Since \( 64 = 4^3 \) or \( 64 = 2^6 \), we can express it as:
\[ \sqrt[3]{\frac{1}{64}} = \sqrt[3]{64^{-1}} = \frac{1}{\sqrt[3]{64}} = \frac{1}{4} \]

### Step 3: Combine the results
Now we can combine the results from Step 1 and Step 2:
\[ \sqrt{225} + \sqrt[3]{\frac{1}{64}} = 15 + \frac{1}{4} \]

### Step 4: Convert \( 15 \) to a fraction
To add these two numbers, we convert \( 15 \) into a fraction with a denominator of \( 4 \):
\[ 15 = \frac{15 \times 4}{4} = \frac{60}{4} \]

### Step 5: Add the fractions
Now we can add the two fractions:
\[ \frac{60}{4} + \frac{1}{4} = \frac{60 + 1}{4} = \frac{61}{4} \]

### Final Answer
Thus, the final answer is:
\[ \sqrt{225} + \sqrt[3]{\frac{1}{64}} = \frac{61}{4} \]