Find the square root of 175.(1 point) simplfy
The square root of 175 can be simplified as follows:
√175 = √(25 * 7)
= √25 * √7
= 5√7
Therefore, the simplified answer is 5√7.
To find the square root of 175, you can use the long division method. Here are the steps:
Step 1: Start with an initial guess. Let's take the square root of 100, which is 10. Divide 175 by 10.
175 ÷ 10 = 17.5
Step 2: Take the average of the guess and the division result. In this case, (10 + 17.5)/2 = 13.75.
Step 3: Divide 175 by the new guess:
175 ÷ 13.75 = 12.72
Step 4: Repeat steps 2 and 3, using the latest division result and the new guess:
(13.75 + 12.72)/2 = 13.235
175 ÷ 13.235 = 13.235
Step 5: Repeat this process until you reach a satisfactory level of accuracy. In this case, after a few more iterations, you will find that the square root of 175 is approximately 13.235.
So, the simplified square root of 175 is approximately 13.235.
To find the square root of 175, you can use a calculator or follow the manual method of finding a square root. Here's how you can manually find the square root:
1. Start by making an educated guess for the square root. In this case, a good guess could be around 13 since 13 * 13 is 169 and 14 * 14 is 196, which are close numbers to 175.
2. Divide 175 by your guess (13). You get the quotient as well as the remainder (175 ÷ 13 = 13 with a remainder of 4).
3. Now, take the quotient (13) and average it with your guess (13) to get a better guess for the square root. To average, add your guess and quotient together and divide by 2 ([13 + 13] ÷ 2 = 13).
4. Repeat steps 2 and 3 until you reach your desired level of accuracy or until there are no more decimal places to evaluate.
The process will look something like this:
- Initial guess: 13
- 175 ÷ 13 = 13 with a remainder of 4
- New guess: ([13 + 13] ÷ 2) = 13
- Updated guess: 13
- 175 ÷ 13 = 13 with a remainder of 4
- New guess: ([13 + 13] ÷ 2) = 13
Since the process of dividing and averaging didn't change the guess anymore, we can conclude that the square root of 175 is approximately 13.
So the square root of 175 is approximately 13.