Question 8 of 29intermediate🔧 ApplyNumerical2 marks

What number will you multiply by 1323 to make it a cube number?

Correct Answer

Step 1: Prime factorisation of 1323 1323 = 3×4413 \times 441 = 3×213 \times 21² = 3 × (3×73 \times 7)² = 3³ × 7²

Step 2: For a perfect cube, all exponents must be multiples of 3. The exponent of 7 is 2, so multiply by 7.

Step 3: 1323×71323 \times 7 = 9261 = 3³ × 7³ = 21³

Answer: Multiply 1323 by 7 to make it a perfect cube.

Exercise: Figure it Out (Section 2) | Q: 2 | (Page Page 16)
For More Understanding

Explanation

The chapter explains that for a number to be a perfect cube, each prime factor must appear a multiple of 3 times. By prime factorisation, we identify factors with exponents not divisible by 3 and multiply accordingly.

Solution Steps

  1. Step 1: Find prime factorisation of 1323

  2. Step 2: 1323 = 3×4413 \times 441 = 3×213 \times 21² = 3 × (3×73 \times 7)² = 3³ × 7²

  3. Step 3: Check exponents: 3 has exponent 3 (multiple of 3), 7 has exponent 2 (not multiple of 3)

  4. Step 4: Multiply by 7 to make exponent of 7 equal to 3

  5. Step 5: 1323×71323 \times 7 = 9261 = 3³ × 7³ = 21³

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