Question

How do you get a square root by prime factorization

Answer 1

Answer:

Step-by-step explanation:

Resolving 484 as the product of primes, we get

484 = 2 × 2 × 11 × 11  

√484 = √(2 × 2 × 11 × 11)  

= 2 × 11

Therefore, √484 = 22

2. Find the square root of 324.  

Solution:

The square root of 324 by prime factorization, we get

324 = 2 × 2 × 3 × 3 × 3 × 3

√324 = √(2 × 2 × 3 × 3 × 3 × 3)

= 2 × 3 × 3

Therefore, √324 = 18

3. Find out the square root of 1764.

Solution:

The square root of 1764 by prime factorization, we get

1764 = 2 x 2 x 3 x 3 x 7 x 7.  

√1764 = √(2 x 2 x 3 x 3 x 7 x 7)

= 2 x 3 x 7

Therefore, √1764 = 42.

4. 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.

5. 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