Find the square of :
`3+2sqrt(5)`

Answer

To find the square of \(3 + 2\sqrt{5}\), we will use the algebraic identity for the square of a binomial, which states:

\[ (a + b)^2 = a^2 + b^2 + 2ab \]

### Step 1: Identify \(a\) and \(b\)
In our case, we can identify:
- \(a = 3\)
- \(b = 2\sqrt{5}\)

### Step 2: Apply the identity
Now we will apply the identity:

\[ (3 + 2\sqrt{5})^2 = 3^2 + (2\sqrt{5})^2 + 2 \cdot 3 \cdot (2\sqrt{5}) \]

### Step 3: Calculate \(a^2\)
Calculate \(3^2\):

\[ 3^2 = 9 \]

### Step 4: Calculate \(b^2\)
Calculate \((2\sqrt{5})^2\):

\[ (2\sqrt{5})^2 = 2^2 \cdot (\sqrt{5})^2 = 4 \cdot 5 = 20 \]

### Step 5: Calculate \(2ab\)
Calculate \(2 \cdot 3 \cdot (2\sqrt{5})\):

\[ 2 \cdot 3 \cdot (2\sqrt{5}) = 12\sqrt{5} \]

### Step 6: Combine all parts
Now combine all the parts together:

\[ (3 + 2\sqrt{5})^2 = 9 + 20 + 12\sqrt{5} \]

### Step 7: Simplify
Combine the constant terms:

\[ 9 + 20 = 29 \]

Thus, we have:

\[ (3 + 2\sqrt{5})^2 = 29 + 12\sqrt{5} \]

### Final Answer
The square of \(3 + 2\sqrt{5}\) is:

\[ 29 + 12\sqrt{5} \]

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