Question 17 of 29intermediate🔧 ApplyNumerical2 marks

Find 36², given that 35² = 1225.

Correct Answer

Pattern: Consecutive squares differ by consecutive odd numbers.

Step 1: The pattern shows n² = (n-1)² + (nth odd number)

Step 2: The nth odd number = 2n - 1

Step 3: For n = 36: 36th odd number = 2×362 \times 36 - 1 = 71

Step 4: 36² = 35² + 71 = 1225 + 71 = 1296

Exercise: Perfect Squares and Odd Numbers | Q: 5 | (Page Page 6)
For More Understanding

Explanation

The chapter explains that the difference between consecutive squares follows the pattern of odd numbers. The nth odd number is 2n - 1. To find 36² from 35², we add the 36th odd number.

Solution Steps

  1. Step 1: The pattern shows n² = (n-1)² + (nth odd number)

  2. Step 2: The nth odd number = 2n - 1

  3. Step 3: For n = 36: 36th odd number = 2×362 \times 36 - 1 = 71

  4. Step 4: 36² = 35² + 71 = 1225 + 71 = 1296

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