Question 2 of 29beginner🔧 ApplyNumerical2 marks

Find the length of the side of a square whose area is 441 m².

Correct Answer

Given: Area of square = side² = 441 m²

Method: Find 441\sqrt{441} using prime factorisation

Calculation: 441 = 3×1473 \times 147 = 3×33 \times 3 × 49 = 3×33 \times 3 × 7×77 \times 7 441 = 3² × 7² = (3×73 \times 7)² = 21²

Answer: side = 441\sqrt{441} = 21 m

Exercise: Figure it Out (Section 1) | Q: 4 | (Page Page 10)
For More Understanding

Explanation

The chapter explains that the square root of a number gives the side length when the area is known. Using prime factorisation, we can determine if a number is a perfect square and find its square root.

Solution Steps

  1. Step 1: Area of square = side² = 441

  2. Step 2: Find 441\sqrt{441} using prime factorisation

  3. Step 3: 441 = 3×1473 \times 147 = 3×33 \times 3 × 49 = 3×33 \times 3 × 7×77 \times 7

  4. Step 4: 441 = (3×73 \times 7)² = 21²

  5. Step 5: Therefore, side = 441\sqrt{441} = 21 m

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