Find the square of :
`(3sqrt(5))/(5)`

Answer

To find the square of \(\frac{3\sqrt{5}}{5}\), we will follow these steps:

1. **Write the expression for squaring**:
We need to find the square of \(\frac{3\sqrt{5}}{5}\). This can be expressed as:
\[ \left(\frac{3\sqrt{5}}{5}\right)^2 \]

2. **Apply the square to the numerator and denominator**:
When squaring a fraction, we square both the numerator and the denominator:
\[ \frac{(3\sqrt{5})^2}{5^2} \]

3. **Calculate the square of the numerator**:
The numerator is \(3\sqrt{5}\). Squaring it gives:
\[ (3\sqrt{5})^2 = 3^2 \cdot (\sqrt{5})^2 = 9 \cdot 5 = 45 \]

4. **Calculate the square of the denominator**:
The denominator is \(5\). Squaring it gives:
\[ 5^2 = 25 \]

5. **Combine the results**:
Now we can combine the squared numerator and denominator:
\[ \frac{45}{25} \]

6. **Simplify the fraction**:
We can simplify \(\frac{45}{25}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
\[ \frac{45 \div 5}{25 \div 5} = \frac{9}{5} \]

Thus, the square of \(\frac{3\sqrt{5}}{5}\) is:
\[ \frac{9}{5} \]