To find the square root of $2916$ using the factorization method, follow these steps:

Step 1: Prime Factorization of $2916$

We divide $2916$ by its smallest prime number repeatedly until we are left with prime factors:

1. $2916 \div 2 = 1458$
2. $1458 \div 2 = 729$
   ($729$ is no longer divisible by $2$, so we proceed with $3$)
3. $729 \div 3 = 243$
4. $243 \div 3 = 81$
5. $81 \div 3 = 27$
6. $27 \div 3 = 9$
7. $9 \div 3 = 3$
8. $3 \div 3 = 1$

Thus, the prime factorization of $2916$ is:

$2916 = 2^2 \times 3^6$

Step 2: Pair the Factors

For square roots, we take one factor from each pair:

$\sqrt{2916} = \sqrt{2^2 \times 3^6}$

Take one $2$ from $2^2$, and three $3$'s from $3^6$:

$\sqrt{2916} = 2 \times 3^3$

Step 3: Simplify

Now calculate $3^3$:

$3^3 = 27$

$\sqrt{2916} = 2 \times 27 = 54$

Final Answer:

$\sqrt{2916} = 54$

Would you like further details or a breakdown of any step? 😊

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Here are five related questions:

1. How is prime factorization used for finding cube roots?
2. What is the square root of $2025$ by the factorization method?
3. How do we verify a square root calculation?
4. Can we use a shortcut to find square roots of perfect squares?
5. What happens if the number is not a perfect square?

Tip: Prime factorization is not only useful for square roots but also for finding greatest common divisors (GCD) and least common multiples (LCM)!