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Solve using method of prime factorization:

$729 =$ [[1]].

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Detailed Solution

Using method of prime factorization,

729 = 27.

The given number is 729.
The prime factorization for 729 is
Question Image

The prime factorization of 729 is,

729 = 3 × 3 × 3 × 3 × 3 × 3.

Making pair the prime factors, we get,

729 = 3 × 3 ¯ × 3 × 3 ¯ × 3 × 3 ¯

Now, taking the product of prime factors, choosing one factor out of every pair, we get,

729 = 3 × 3 × 3 = 27.

Thus, the square root of 729 is 27.

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