let’s calculate the square root of 484 in detail

calculate the square root of 484 –

Step 1: Prime Factorization of 484

To find the square root of 484, it’s helpful to start by expressing 484 as a product of its prime factors. The prime factorization of 484 is:

484 = 2² × 11²

Step 2: Using the Prime Factorization to Simplify the Square Root

Since 484 can be expressed as a product of identical prime factors raised to the power of 2, we can simplify the square root as follows:

√484 = √(2² × 11²)

Using the property of square roots (√(a × b) = √a × √b), we can split the square root into two separate square roots:

√484 = √(2²) × √(11²)

Simplifying each square root:

√484 = 2 × 11

Step 3: Calculating the Result

Now, we can simply multiply the two values together:

√484 = 2 × 11 = 22

Conclusion

The square root of 484 is 22. This means that when you multiply 22 by itself (22 × 22), you get 484. The detailed process involved recognizing the prime factorization of 484, using the properties of square roots to simplify the expression, and then performing the multiplication to arrive at the final result of 22.