Question

$134^2=?$

• A. 17956
• B. 17962
• C. 17566
• D. 17546

Answer 1

Answer:

A. 17956

Understanding Squares and Their Calculation

• Calculating the square of a number, denoted as $n^2$, means multiplying the number by itself (n × n). For example, $134^2$ means $134 × 134$.

Methods for Calculating Squares:

• Direct Multiplication: This is the most straightforward method. For $134^2$, you perform $134 × 134$ column multiplication.

• Using Algebraic Identity $(a+b)^2 = a^2 + 2ab + b^2$:
  This method is highly useful for competitive exams as it can simplify calculations.

  • To calculate $134^2$, you can split 134 into $(130 + 4)$ or $(100 + 34)$.

  • Using $(130 + 4)^2$:
    Here, $a = 130$ and $b = 4$.
    $a^2 = 130^2 = 16900$
    $2ab = 2 × 130 × 4 = 260 × 4 = 1040$
    $b^2 = 4^2 = 16$
    Adding these values: $16900 + 1040 + 16 = 17956$.

  • Using $(100 + 34)^2$:
    Here, $a = 100$ and $b = 34$.
    $a^2 = 100^2 = 10000$
    $2ab = 2 × 100 × 34 = 200 × 34 = 6800$
    $b^2 = 34^2 = 1156$
    Adding these values: $10000 + 6800 + 1156 = 17956$.