Question 1 of 29intermediate🔧 ApplyMCQ1 mark

Given 125² = 15625, what is the value of 126²?

Exercise: Figure it Out (Section 1) | Q: 3 | (Page Page 10)
For More Understanding

Explanation

The chapter explains that consecutive squares differ by consecutive odd numbers. The pattern shows that (n+1)² = n² + (2n+1). For n = 125: 126² = 125² + (2×1252 \times 125 + 1) = 15625 + 251 = 15876. Alternatively, using the odd number pattern, the 126th odd number is 2×1262 \times 126 - 1 = 251, so 126² = 125² + 251.

Solution Steps

  1. Step 1: Use the formula (n+1)² = n² + 2n + 1

  2. Step 2: For n = 125: 126² = 125² + 2×1252 \times 125 + 1

  3. Step 3: 126² = 15625 + 250 + 1 = 15625 + 251

  4. Step 4: Therefore, option (iv) 15625 + 251 is correct

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