Question

$156^2=?$

• A. 22716
• B. 24336
• C. 23336
• D. 24436

Answer 1

Answer:

B. 24336

Methods to Calculate Squares

• To calculate the square of a number, say N, means to multiply the number by itself (N × N or N²).

• Understanding square calculations is fundamental in competitive exams for topics like algebra, geometry, area calculations, and data interpretation.

Method 1: Direct Multiplication

• This is the most straightforward method, involving multiplying 156 by 156.

1. Multiply 156 by 6: 156 × 6 = 936

2. Multiply 156 by 50: 156 × 50 = 7800 (or 156 × 5 = 780, then add a zero)

3. Multiply 156 by 100: 156 × 100 = 15600

4. Add the results: 936 + 7800 + 15600 = 24336

Method 2: Using Algebraic Identity (a+b)²

• This method can simplify calculations for larger numbers by breaking them into simpler parts.

• The identity is (a + b)² = a² + 2ab + b².

• For 156², we can write it as (150 + 6)² or (160 - 4)². Let's use (150 + 6)².

1. Here, a = 150 and b = 6.

2. Calculate a²: 150² = 22500 (since 15² = 225, 150² = 225 with two zeros).

3. Calculate 2ab: 2 × 150 × 6 = 300 × 6 = 1800.

4. Calculate b²: 6² = 36.

5. Add the results: 22500 + 1800 + 36 = 24336.

Method 3: Unit Digit Check (for Multiple Choice Questions)

• When solving multiple-choice questions, the unit digit of the square can often help eliminate incorrect options quickly.

• The unit digit of 156 is 6.

• The unit digit of 156² will be the unit digit of 6², which is 36. So, the unit digit of the final answer must be 6.

• This method is particularly useful if the options provided have different unit digits.