Prime Exponents and Square Perimeters

Prime Exponents and Square Perimeters

IP 1
6 marks
  1. The numbers \(A\), \(B\) and \(C\), written as products of their prime factors, are given below, where \(p\), \(q\) and \(r\) are prime numbers.
    \(A=p^5\times q^4\times r^8\)
    \(B=p^4\times q^5\times r^4\)
    \(C=3^3\times5^2\times11\)
    Using the prime factors given above, find
    1. the cube root of \(A\times B\),[2]
    2. the smallest positive integer, \(k\), such that \(\frac{C}{k}\) is a perfect square.[1]
  2. The area of a square is \(3\,600\text{ cm}^2\). Using prime factorisation, find the perimeter of the square.[3]

Solution:

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Answer:(a)(i) \(p^3q^3r^4\) (ii) \(k=33\) (b) \(240\text{ cm}\)

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