Question

Square root of 23658 by factor mathod

Answer 1

23658 = 2*3*3943
there are no repeated prime factors, so the factor method doesn't really work well here.

Answer 2

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.

Answer 3

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.