Arrange `root(4)(3),root(3)(2)androot(6)(5)` in the decreasing order.

Answer

To arrange \( \sqrt[4]{3}, \sqrt[3]{2}, \) and \( \sqrt[6]{5} \) in decreasing order, we can follow these steps:

### Step 1: Rewrite the roots in exponent form
We start by rewriting each root in exponent form:
- \( \sqrt[4]{3} = 3^{1/4} \)
- \( \sqrt[3]{2} = 2^{1/3} \)
- \( \sqrt[6]{5} = 5^{1/6} \)

### Step 2: Find a common denominator for the exponents
To compare these values, we need to express them with a common denominator. The denominators are 4, 3, and 6. The least common multiple (LCM) of these numbers is 12.

### Step 3: Convert each exponent to have the common denominator
Now we convert each exponent to have a denominator of 12:
- For \( 3^{1/4} \):
\[ 3^{1/4} = 3^{3/12} \]
- For \( 2^{1/3} \):
\[ 2^{1/3} = 2^{4/12} \]
- For \( 5^{1/6} \):
\[ 5^{1/6} = 5^{2/12} \]

### Step 4: Compare the values
Now we can compare the values:
- \( 3^{3/12} \)
- \( 2^{4/12} \)
- \( 5^{2/12} \)

### Step 5: Calculate the approximate values
To compare these values more easily, we can calculate their approximate values:
- \( 3^{3/12} \approx 1.316 \)
- \( 2^{4/12} \approx 1.587 \)
- \( 5^{2/12} \approx 1.245 \)

### Step 6: Arrange in decreasing order
Based on the approximate values:
1. \( 2^{4/12} \) (which corresponds to \( \sqrt[3]{2} \))
2. \( 3^{3/12} \) (which corresponds to \( \sqrt[4]{3} \))
3. \( 5^{2/12} \) (which corresponds to \( \sqrt[6]{5} \))

Thus, the order in decreasing form is:
\[ \sqrt[3]{2} > \sqrt[4]{3} > \sqrt[6]{5} \]

### Final Answer
In the original form, the arrangement is:
\[ \sqrt[3]{2} > \sqrt[4]{3} > \sqrt[6]{5} \]