Find the square root of 175
The square root of 175 is approximately 13.23
To find the square root of 175, follow these steps:
Step 1: Estimate the Square Root
You can start by estimating the square root of 175. The nearest perfect square numbers to 175 are 169 (13^2) and 196 (14^2). Since 175 is closer to 169, we can estimate that the square root of 175 is approximately 13.
Step 2: Use Newton's Method (Optional)
If you want a more accurate calculation, you can use Newton's method. However, this step is optional.
Newton's method formula:
x(n+1) = x(n) - (f(x(n)) / f'(x(n)))
For f(x) = x^2 - 175, the derivative f'(x) = 2x.
Let's choose an initial estimate x(0) = 13 and perform one iteration:
x(1) = 13 - ((13^2 - 175) / (2 * 13))
= 13 - (169 - 175) / 26
= 13 - 6 / 26
= 13 - 0.23
= 12.77
Step 3: Choose a Greater Accuracy Method (Optional)
If you want an even more accurate calculation, you can use methods like the Babylonian method or bisection method. However, this step is also optional.
Step 4: Verify the Calculation (Optional)
Once you have a more accurate square root estimation, you can verify it by squaring it and checking if the result is approximately 175.
Using the estimation 12.77,
12.77^2 = 163.2329
So, the square root of 175 is approximately 12.77 (or approximately 13 if you only want an estimation).
To find the square root of 175, you can use a calculator or follow these steps to approximate the answer:
1. Start by taking a guess. Since 175 is a relatively large number, you can start with a guess of 10.
2. Square your guess. Multiply 10 by 10 to get 100.
3. Compare your squared guess to 175. Since 100 is less than 175, you know that the square root of 175 is greater than 10.
4. Adjust your guess. Increase your guess by a small amount, say 1. So, your new guess is 11.
5. Square your new guess. Multiply 11 by 11 to get 121.
6. Compare your new squared guess to 175. Since 121 is less than 175, you know that the square root of 175 is greater than 11.
7. Repeat steps 4 to 6, increasing your guess and comparing the squared guess to 175, until you find a close approximation.
Using this method, you will find that the square root of 175 is approximately 13.23.