Calculating the Square of 11211

The question asks us to find the square of the number 11211. Squaring a number means multiplying the number by itself. So, we need to calculate \(11211 \times 11211\).

This calculation involves multiplying a five-digit number by itself.

Step-by-Step Squaring Calculation

We can find the square of 11211 by performing long multiplication:

\(11211 \times 11211\)

We multiply 11211 by each digit of the multiplier 11211, starting from the rightmost digit (units place), and then add the results, shifting each subsequent result one place to the left.

• Multiply 11211 by 1 (units digit): \(11211 \times 1 = 11211\)
• Multiply 11211 by 1 (tens digit, value 10): \(11211 \times 10 = 112110\)
• Multiply 11211 by 2 (hundreds digit, value 200): \(11211 \times 200 = 2242200\)
• Multiply 11211 by 1 (thousands digit, value 1000): \(11211 \times 1000 = 11211000\)
• Multiply 11211 by 1 (ten thousands digit, value 10000): \(11211 \times 10000 = 112110000\)

Now, we add these partial products:

\(11211 + 112110 + 2242200 + 11211000 + 112110000\)

Adding the partial products carefully, we get 125686521.

Result of Squaring 11211

The square of 11211 is 125686521. This is the result of multiplying 11211 by itself.

\(11211^2 = 125686521\)

Comparing Result with Options

We compare our calculated value with the given options:

• Option 1: 123432171
• Option 2: 125686521
• Option 3: 122331151
• Option 4: 123454321

Our calculated result, 125686521, exactly matches Option 2.

Revision Table: Squaring Numbers and Patterns

Understanding squares can be helped by looking at patterns. Here are squares of some numbers:

Numbers consisting only of the digit '1' follow a specific pattern when squared, but 11211 includes a '2', altering this pattern.

Additional Information: Properties of Squares

A square number, also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 25 is a perfect square because it is \(5 \times 5\). The units digit of a perfect square can only be 0, 1, 4, 5, 6, or 9. The number 11211 ends in 1, and its square, 125686521, also ends in 1, which is consistent with this property.