Question 16 of 29beginner💡 UnderstandShort Answer2 marks

What can you say about the parity of a number and its square?

Correct Answer

The parity of a number and its square is always the same.

Step 1: Consider an even number n = 2k

Step 2: n² = (2k)² = 4k², which is even

Step 3: Consider an odd number m = 2k + 1

Step 4: m² = (2k+1)² = 4k² + 4k + 1 = 2(2k² + 2k) + 1, which is odd

∴ If a number is even, its square is even. If a number is odd, its square is odd.

Exercise: Patterns and Properties of Perfect Squares | Q: 4 | (Page Page 5)
For More Understanding

Explanation

The chapter discusses properties of squares including parity. When we multiply two even numbers, the result is even. When we multiply two odd numbers, the result is odd. Since a square is a number multiplied by itself, the parity is preserved.

Solution Steps

  1. Step 1: Consider an even number n = 2k

  2. Step 2: n² = (2k)² = 4k², which is even

  3. Step 3: Consider an odd number m = 2k + 1

  4. Step 4: m² = (2k+1)² = 4k² + 4k + 1 = 2(2k² + 2k) + 1, which is odd

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