1. Square Roots

2. Square Roots
The Square Root of a number is the number you can multiply by itself to give you that number.
Thus, = 2, because 22=4
= 3, because 32=9
Try:
= 8, because 82=64
= 12, because 122=144
= 1, because 12 = 1
= 0, because 02 = 0

3. Square Root - Prime Factorization Method
To find the square root using the prime factorization method Step I:  Resolve the given number into prime factors.  Step II:  Make pairs of similar factors.  Step III:  Take the product of prime factors, choosing one factor out of every pair.

4. 1. Find the square root of 484 by prime factorization method.
Solution:
Resolving 484 as the product of primes, we get
484 = 2 × 2 × 11 × 11 
√484 = √(2 × 2 × 11 × 11) 
= 2 × 11
Therefore, √484 = 22

5. Evaluate √4356 Solution:
By using prime factorization, we get 
4356 = 2 x 2 x 3 x 3 x 11 x 11
√4356 = √(2 x 2 x 3 x 3 x 11 x 11)
= 2 × 3 × 11
Therefore, √4356 = 66.

6. Evaluate √11025
Solution:
By using prime factorization, we get
11025 = 5 x 5 x 3 x 3 x 7 x 7. 
√11025 = √(5 x 5 x 3 x 3 x 7 x 7)
= 5 × 3 × 7
Therefore, √11025 = 105