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Home >> Square Root >> Square Root by Prime Factorization Method >>

Square Root by Prime Factorization Method

Square Root by Repeated Subtraction Method Square Root by Prime Factorization Method Square Root by Long Division Method

Before you understand how to find Square Root by Prime Factorization Method topic, you are advice to read:

What is Square Root ?
What is Prime Factorization Method ?

Steps of finding Square root by prime factorization method:

Step 1: Prime Factorization of given number
Step 2: Pair the same prime factors
Step 3: Collect one prime factor from each pair
Step 4: Multiply the collected prime factors ( if only one pair, ignore this step)
Step 5: Resultant number is the square root of the given number

Example 1: Find square root of 16 using prime factorization method.
Solution: Steps are as follows:

Step 1: Prime Factorization of given number 16 and we get:
16 = 2 X 2 X 2 X 2

Step 2: Pair the same prime factors and we get:
= 2 X 2 X 2 X 2

Step 3: Collect one prime factor from each pair and we get:
= 2 X 2

Step 4: Multiply the collected prime factors and we get:
= 4

Step 5: Resultant number is the square root of the given number and we write it as:
  16   = 4



Example 2: Find square root of 81 using prime factorization method.
Solution: Steps are as follows:

Step 1: Prime Factorization of given number 81 and we get:
81 = 3 X 3 X 3 X 3

Step 2: Pair the same prime factors and we get:
= 3 X 3 X 3 X 3

Step 3: Collect one prime factor from each pair and we get:
= 3 X 3

Step 4: Multiply the collected prime factors and we get:
= 9

Step 5: Resultant number is the square root of the given number and we write it as:
  81   = 9

Example 3: Find square root of 121 using prime factorization method.
Solution: Steps are as follows:

Step 1: Prime Factorization of given number 121 and we get:
121 = 11 x 11

Step 2: Pair the same prime factors and we get:
= 11 X 11

Step 3: Collect one prime factor from each pair and we get:
= 11

Step 4: Resultant number is the square root of the given number and we write it as:
  121   = 11



Example 4: Find square root of 100 using prime factorization method.
Solution: Steps are as follows:

Step 1: Prime Factorization of given number 100 and we get:
100 = 2 X 2 X 5 X 5

Step 2: Pair the same prime factors and we get:
= 2 X 2 X 5 X 5

Step 3: Collect one prime factor from each pair and we get:
= 2 X 5

Step 4: Multiply the collected prime factors and we get:
= 10

Step 5: Resultant number is the square root of the given number and we write it as:
  100   = 10



Example 5: Find square root of 1296 using prime factorization method.
Solution: Steps are as follows:

Step 1: Prime Factorization of given number 1296 and we get:
1296 = 2 X 2 X 2 X 2 X 3 X 3 X 3 X 3

Step 2: Pair the same prime factors and we get:
= 2 X 2 X 2 X 2 X 3 X 3 X 3 X 3

Step 3: Collect one prime factor from each pair and we get:
= 2 X 2 X 3 X 3

Step 4: Multiply the collected prime factors and we get:
= 36

Step 5: Resultant number is the square root of the given number and we write it as:
  1296   = 36

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