Understanding the Question: Square Root of a Percentage

The question asks us to find the value that, when multiplied by itself, equals 64%. This is known as finding the square root of 64%.

Step-by-Step Calculation

To solve this, we first need to convert the percentage into a more manageable form, like a decimal or a fraction.

1. Convert Percentage to Decimal:

   The percentage 64% can be written as a decimal by dividing by 100:

   \(64\% = \frac{64}{100} = 0.64\)

2. Calculate the Square Root:

   Now, we need to find the square root of the decimal value 0.64.

   We are looking for a number 'x' such that \(x \times x = 0.64\).

   We know that \(8 \times 8 = 64\). Therefore, thinking about decimals:

   \(0.8 \times 0.8 = 0.64\)

   So, the square root of 0.64 is 0.8:

   \(\sqrt{0.64} = 0.8\)

3. Convert the Result Back to Percentage:

   The result we found is 0.8. To express this as a percentage, we multiply by 100:

   \(0.8 \times 100 = 80\%\)

Conclusion

Therefore, the square root of 64% is 80%. This means that if you multiply 80% by itself, you get 64%.

\(80\% \times 80\% = 0.8 \times 0.8 = 0.64 = 64\%\)