The simplified form of 72 is 62.
To simplify 72, we begin by determining its prime factors. We can break down 72 as follows:
72=2×36=2×2×18=2×2×2×9=2×2×2×3×3.Next, we can group the prime factors in pairs, resulting in:
(2×2)×(3×3)×2.
Each pair of identical factors can be taken out of the square root as a single number. Therefore, we have:
72=(22)×(32)×2=2×3×2=62.This indicates that the square root of 72 can be expressed as 6 times the square root of 2.
The technique of simplifying square roots by factoring them into prime numbers and then grouping pairs is a valuable skill in GCSE Maths. This method allows for the transformation of complex square roots into simpler forms, making them easier to handle in subsequent calculations.
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