**Finding Squares and Square Roots**

Finding squares and square roots are mathematical operations that involve manipulating numbers to determine their values. Squaring a number means multiplying it by itself, while finding the square root of a number means finding the value that, when multiplied by itself, gives the original number. Let's explore each of these operations in detail:

**Finding Squares:**

To find the square of a number, follow these steps:

1. **Multiply the number by itself:** Take the given number and multiply it by itself. For example, if you want to find the square of 3, multiply 3 by 3: 3 * 3 = 9.
2. **The result is the square:** The product obtained from step 1 is the square of the given number. In this case, the square of 3 is 9.

It is also possible to find the square of a number using exponents. In this case, you raise the number to the power of 2:

1. **Raise the number to the power of 2:** Write the given number with a superscript 2, indicating that it is being squared. For example, 3^2.
2. **Evaluate the expression:** Calculate the value of the expression. In this case, 3^2 equals 9.

**Finding Square Roots:**

To find the square root of a number, follow these steps:

1. **Start with the given number:** Take the number for which you want to find the square root. For example, if you want to find the square root of 16, start with 16.
2. **Make an initial guess:** Make an initial guess for the square root. For simplicity, let's start with a guess of 2.
3. **Divide the given number by the guess:** Divide the given number by the initial guess. In this case, 16 ÷ 2 = 8.
4. **Average the guess and the result:** Take the average of the guess and the result obtained from the previous step. In this case, the average of 2 and 8 is (2 + 8) ÷ 2 = 5.
5. **Repeat steps 3 and 4:** Continue dividing the given number by the average obtained in step 4 and averaging the guess and the result until you reach a satisfactory level of accuracy.
6. **Converge to the square root:** As you repeat steps 3 and 4, you will eventually converge to a value that is very close to the square root of the given number. In this case, the square root of 16 is approximately 4.

It is important to note that finding square roots can be a complex process, especially for large numbers. However, there are mathematical algorithms and methods, such as the Newton-Raphson method, that can be used to find square roots with increased precision.

In conclusion, finding squares and square roots involves multiplying a number by itself or finding the value that, when multiplied by itself, gives the original number. By following the steps outlined above, you can calculate these values accurately.

We can find square root by factorication method and long division method and squares multiple the no. by itself