Find the sub-triplicate ratio of `27:125`?

Options

A. `9/25`
B. `3/5`
C. 0.36
D. 0.6

Answer

To find the sub-triplicate ratio of \(27:125\), we need to follow these steps:

### Step 1: Understand the concept of sub-triplicate ratio
The sub-triplicate ratio of two numbers \(a\) and \(b\) is found by taking the cube roots of both numbers. The sub-triplicate ratio can be expressed as:
\[ \text{Sub-triplicate ratio} = \sqrt[3]{a} : \sqrt[3]{b} \]

### Step 2: Identify the numbers
In this case, we have:
- \(a = 27\)
- \(b = 125\)

### Step 3: Calculate the cube root of \(27\)
To find the cube root of \(27\):
\[ \sqrt[3]{27} = 3 \]
This is because \(3 \times 3 \times 3 = 27\).

### Step 4: Calculate the cube root of \(125\)
Next, we find the cube root of \(125\):
\[ \sqrt[3]{125} = 5 \]
This is because \(5 \times 5 \times 5 = 125\).

### Step 5: Form the sub-triplicate ratio
Now that we have both cube roots, we can form the sub-triplicate ratio:
\[ \text{Sub-triplicate ratio} = \sqrt[3]{27} : \sqrt[3]{125} = 3 : 5 \]

### Step 6: Convert the ratio to a fraction
The ratio \(3:5\) can also be expressed as a fraction:
\[ \frac{3}{5} \]

### Conclusion
Thus, the sub-triplicate ratio of \(27:125\) is \(3:5\) or \(\frac{3}{5}\).

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