Square root of 23658 by factor mathod
23658 = 2*3*3943
there are no repeated prime factors, so the factor method doesn't really work well here.
You are correct. The factor method works best for numbers that have perfect square factors, which can be simplified using the method. However, in the case of 23658, it does not have perfect square factors and therefore cannot be simplified using the factor method. In this case, we can use other methods to find the square root of 23658, such as by using a calculator or approximating the answer.
To find the square root of 23658 using the factoring method, follow these steps:
Step 1: Prime Factorize
Find the prime factorization of 23658, which is the process of breaking it down into its prime factors.
23658 = 2 × 3 × 7 × 563
Step 2: Pair Factors
Pair up the prime factors in pairs, starting from the lowest prime number, and multiply each pair together.
In this case, we have: (2 × 7) × (3 × 563)
Step 3: Combine Pairs
Combine the pairs by multiplying them together.
(2 × 7) × (3 × 563) = 14 × 1689
Step 4: Simplify
Keep simplifying until you cannot simplify any further.
14 × 1689 = 23646
Step 5: Determine Square Root
The square root of 23658 is the product of the primes that were paired together:
√23658 = 2 × 7 × √1689
So, the square root of 23658 by the factoring method is 2 × 7 × √1689.
To find the square root of 23658 by the factor method, we need to first factor the number into perfect square factors.
Let's start by dividing 23658 by 4:
- 4 is a perfect square, and 23658 ÷ 4 = 5914.5
Now we look for perfect square factors of 5914.5:
- We can divide by 4 again: 5914.5 ÷ 4 = 1478.625
- No other perfect square factors can be found, so we move on to the next step.
We can now express 23658 as a product of its perfect square factors and take the square root of each factor:
Square root of 23658 = √(4 x 4 x 1478.625)
= 2 x 2 x √1478.625
Now we need to simplify √1478.625:
- We can divide by 4 again: √1478.625 = √(4 x 369.65625)
= 2 x √369.65625
Then, we simplify √369.65625:
- We can divide by 4 again: √369.65625 = √(4 x 92.4140625)
= 2 x √92.4140625
Finally, we simplify √92.4140625:
- We can divide by 4 again: √92.4140625 = √(4 x 23.103515625)
= 2 x √23.103515625
This is the simplified form of the square root of 23658.