Worked Example 1
Find the cube root of 1728 by prime factorisation.
Step 1: break it into primes1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
Step 2: group in THREES(2 × 2 × 2), (2 × 2 × 2), (3 × 3 × 3)
Step 3: take one from each group2 × 2 × 3 = 12
Check both ways12 × 12 × 12 = 1728. And 1728 ends in 8, so the root must end in 2, which it does.
Worked Example 2
Find the cube root of 262144 using the two block method.
Split into blocks of three from the right262144 becomes 262 and 144.
The right block gives the last digit144 ends in 4, and only 8 cubed ends in 4, so the root ends in 8.
The left block gives the first digit262 lies between 6³ and 7³, so the root begins with 6.
Put them togetherThe cube root of 262144 is 68, far quicker than factorising a six digit number.
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