What is 125−−−√ simplified
The square root of 125 is not a rational number, so it cannot be simplified further. However, it can be written as 5√5 in radical form.
To simplify the expression 125−−−√, we need to find the square root of 125.
The square root of 125 is equal to √(125).
To simplify, we can break down 125 into its prime factors: 125 = 5 * 5 * 5.
Since the square root of each factor is 5, we can simplify √(125) as 5 * 5 * √(5).
Therefore, the simplified form of 125−−−√ is 5√(5).
To simplify the expression 125 −√, first, let's find the square root of 125.
We know that the square root of 125 is the value that, when multiplied by itself, results in 125. To find the square root, we can use a calculator or follow these steps:
1. Start by guessing the square root. In this case, let's guess 10.
2. Square your guess: 10 * 10 = 100.
3. Since our guess is too low, let's try a slightly higher guess. Let's try 11.
4. Square your new guess: 11 * 11 = 121.
5. This time, our guess is too high. So, the square root of 125 must be between 10 and 11.
6. To get a more accurate result, we can try an average between 10 and 11: (10 + 11) / 2 = 10.5.
7. Square your new guess: 10.5 * 10.5 = 110.25.
8. Since our new guess is too low, we need to try a higher guess, such as 10.6.
9. Square your new guess: 10.6 * 10.6 = 112.36.
10. This time, our guess is too high. Thus, the square root of 125 is between 10.5 and 10.6.
By repeating steps 6 to 10 with smaller increments, we can narrow down the range and find a more accurate result. Calculating the square root of 125, we find that it is approximately 11.18034.
Now, let's simplify the expression 125 −√:
125 −√ = 125 − 11.18034
Calculating the subtraction:
125 − 11.18034 ≈ 113.81966
Therefore, the simplified form of 125 −√ is approximately 113.81966.