Solved Example on Prime Factorization and Repeated Subtraction Method
Example: Find the square root of 7056 using prime factorization.
Solution:
7056 = 24 Γ 32 Γ 72
β 7056 = (2 Γ 2) Γ (2 Γ 2) Γ (3 Γ 3) Γ (7 Γ 7)
Take one factor from each pair: 2 Γ 2 Γ 3 Γ 7 = 84
Thus, β7056 = 84
So, the square root of 7056 is 84.
Example: Find the square root of 144 using prime factorization.
Solution:
144 = 24 Γ 32
β 144 = (2 Γ 2) Γ (2 Γ 2) Γ (3 Γ 3)
Take one factor from each pair: 2 Γ 3 = 6
Thus, β144 = 12
So, the square root of 144 is 12.
Example: Find the square root of 4900 using prime factorization.
Solution:
4900 = 22 Γ 52 Γ 72
β 4900 = (2 Γ 2) Γ (5 Γ 5) Γ (7 Γ 7)
Take one factor from each pair: 2 Γ 5 Γ 7 = 70
Thus, β4900 = 70
So, the square root of 4900 is 70.
Example: Find the square root of 121 by repeated subtraction.
Solution:
Start with the given number: 121.
Subtract consecutive odd numbers starting from 1 until reaching zero:
- 121 β 1 = 120
- 120 β 3 = 117
- 117 β 5 = 112
- 112 β 7 = 105
- 105 β 9 = 96
- 96 β 11 = 85
- 85 β 13 = 72
- 72 β 15 = 57
- 57 β 17 = 40
- 40 β 19 = 21
- 21 β 21 = 0
Count the number of times you subtracted an odd number: 11.
The square root of 121 is the number of times you subtracted, which is 11.
So, the square root of 121 is 11.
Finding Square Root Through Prime Factorization and Repeated Subtraction
Square Root is the one of the many arithmetic operations in mathematics. Square root can be calculated using various methods in mathematics such as long division, prime factorization, repeated subtraction, etc. In this article, we will discuss methods of calculation of square root using prime factorization and repeated subtraction method.
Table of Content
- What are Square Roots?
- Square Root by Prime Factorization
- Square Root by Repeated Subtraction
- FAQs