Square root of 175
The square root of 175 is approximately 13.23.
To find the square root of 175, you can follow these steps:
Step 1: Start by making an educated guess for the square root. Since the square root of 169 is 13 and the square root of 196 is 14, we can assume that the square root of 175 is somewhere between 13 and 14.
Step 2: Take the average of the two numbers to refine your guess. The average of 13 and 14 is 13.5.
Step 3: Multiply your refined guess by itself to check if it is close to 175. 13.5 multiplied by 13.5 equals 182.25, which is greater than 175.
Step 4: Take a slightly smaller number than your refined guess and repeat the process. Let's try 13.4.
Step 5: Multiply 13.4 by itself: 13.4 multiplied by 13.4 equals 179.56, which is still greater than 175.
Step 6: Keep refining your guess by trying slightly smaller numbers. Repeat the process until you find an answer that is close to 175.
After following these steps, you will find that the square root of 175 is approximately 13.23.
To find the square root of 175, you can use a scientific calculator or a math software program. However, I will explain the steps you can take to find the square root manually.
Step 1: Start by recognizing that 175 is not a perfect square (meaning it doesn't have an integer square root).
Step 2: Find two perfect squares between which 175 falls. The perfect squares smaller than 175 are 169 (13 x 13) and 144 (12 x 12).
Step 3: Take the square root of the smaller perfect square, which is √169 = 13.
Step 4: Divide 175 by the square root you found in step 3: 175 / 13 = 13.461538.
Step 5: Take the average of the quotient from step 4 and the square root you found in step 3: (13 + 13.461538) / 2 ≈ 13.230769.
Step 6: Repeat steps 4 and 5 using the average found in step 5 and the original number (175), until you achieve the desired level of accuracy.
By following these steps, you will get an approximate answer for the square root of 175, where √175 ≈ 13.230769.