To find the square root of a non-perfect square number using prime factorization, you can follow these steps:
1. Start by finding the prime factorization of the given number.
2. Divide the exponents of the prime factors by 2 (since you're looking for the square root).
3. Multiply these reduced exponents back together to get the square root.
Let's illustrate this with an example:
Suppose you want to find the square root of 180 using prime factorization.
1. Prime factorization of 180:
180 = 2^2 * 3^2 * 5
2. Reduce the exponents by half:
Square root of 180 = 2^(2/2) * 3^(2/2) * 5^(1/2)
3. Calculate the reduced exponents:
Square root of 180 = 2^1 * 3^1 * √5
Now, multiply these reduced exponents together:
Square root of 180 = 2 * 3 * √5 = 6√5
So, the square root of 180 using prime factorization is 6√5.
Негізгі бет Square root of non perfect square numbers | by prime factorization
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