Find the square root of 175.(1 point)
The square root of 175 is approximately 13.228.
To find the square root of 175, follow these steps:
Step 1: Start by setting up the prime factorization of 175:
175 = 5 × 5 × 7
Step 2: Next, group the prime factors in pairs:
175 = (5 × 5) × 7
Step 3: Take one number from each pair and remove it from the square root:
175 = 5 × √(5 × 7)
Step 4: Simplify the square root inside the parentheses:
175 = 5 × √35
Therefore, the square root of 175 is 5√35.
To find the square root of 175, you can follow these steps:
Step 1: Start by guessing the square root. In this case, let's guess that the square root of 175 is around 13.
Step 2: Square the guess. 13 multiplied by 13 is equal to 169.
Step 3: Compare the squared guess to 175. Since 169 is less than 175, we need to increase our guess.
Step 4: Adjust the guess. Increase the guess by a small amount, let's say 0.1, making the new guess 13.1.
Step 5: Square the new guess. 13.1 multiplied by 13.1 is approximately 171.61.
Step 6: Compare the squared guess to 175. Since 171.61 is still less than 175, we need to increase our guess again.
Step 7: Repeat steps 4-6 until your squared guess is very close to 175.
By repeating steps 4-6 a few more times, you will eventually find that the square root of 175 is approximately 13.229.
So, the square root of 175 is approximately 13.229.