The surd form of 72 is 62.
To express 72 in its simplest surd form, we start by factorizing 72 into its prime factors. The prime factorization of 72 is given by 2×2×2×3×3, which can be represented as 23×32. To simplify the square root, we need to identify pairs of prime factors. Each pair of identical numbers can be taken out of the square root as a single number.
In this case, we have one pair of 2s, represented as 22, and one pair of 3s, represented as 32. When we extract these pairs from the square root, we multiply them together: 2×3, which equals 6. The remaining factor inside the square root is 2, since we have one 2 left over from the factorization. Consequently, we find that 72 simplifies to 62.
This process illustrates that surds provide a method for expressing irrational numbers in their simplest form. By breaking down the number into its prime factors and simplifying, we make calculations more manageable. The objective is to express the number in a way that the square root is as simplified as possible, while retaining any irrational components within the square root.
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