Worked Example 1
Find the square root of 576 by prime factorisation.
Step 1: break it into primes576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
Step 2: make pairs(2 × 2), (2 × 2), (2 × 2), (3 × 3). Every factor has a partner.
Step 3: take one from each pair2 × 2 × 2 × 3 = 24
Check24 × 24 = 576. And 20² = 400 while 25² = 625, so an answer between 20 and 25 was expected.
Worked Example 2
What is the smallest number 720 must be multiplied by to make a perfect square?
Factorise720 = 2 × 2 × 2 × 2 × 3 × 3 × 5
Look for the lonely factorThe 2s and 3s pair up, but the 5 has no partner.
Supply the partnerMultiply by 5. 720 × 5 = 3600, and √3600 = 60.
The same idea backwardsIf asked to DIVIDE instead, the answer is also 5: removing the lonely factor leaves 144, which is 12².
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