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


