What is the square root of 45
The square root of 45 is approximately 6.708203932499369.
To find the square root of 45, follow these steps:
Step 1: Start with an initial guess. Let's start with 6.
Step 2: Square the initial guess. 6^2 = 36.
Step 3: Compare the squared guess with the original number. 36 is less than 45.
Step 4: Increase the guess by 1. Our new guess is now 7.
Step 5: Square the new guess. 7^2 = 49.
Step 6: Compare the squared guess with the original number. 49 is greater than 45.
Step 7: We know that the square root of 45 is between 6 and 7.
Step 8: Find the average of the two guesses to narrow down the range. The average of 6 and 7 is 6.5.
Step 9: Square the average. 6.5^2 = 42.25.
Step 10: Compare the squared average with the original number. 42.25 is less than 45.
Step 11: Increase the lower bound by setting it to be the average, 6.5.
Step 12: Repeat steps 4-10 using the new lower bound.
Using these steps and repeating the process, it can be found that the square root of 45 is approximately 6.708.
To find the square root of 45, you can use a calculator or carry out the calculation manually. Here's how you can calculate it manually:
1. Start by making an estimate: Since the square root of 45 is between the square roots of 36 (which is 6) and 49 (which is 7), we know that √45 is between 6 and 7.
2. Next, take the average of the two numbers (6 and 7) to get a better estimate: (6 + 7) / 2 = 6.5.
3. Square 6.5: 6.5 x 6.5 = 42.25.
4. Since 42.25 is less than 45, we know that our estimate is too low.
5. Adjust your estimate: Since our initial estimate was too low, we can increase our new estimate. Let's adjust by 0.1 and make our new estimate 6.6.
6. Square 6.6: 6.6 x 6.6 = 43.56.
7. Our new estimate (6.6) still falls short, so let's adjust again by 0.01. Our new estimate is 6.61.
8. Square 6.61: 6.61 x 6.61 = 43.8121.
9. Now we have a square value that is slightly greater than 45, so our estimate is still too low.
10. Continue this process of refining your estimate by adjusting and squaring until you reach a satisfactory approximation. You will find that the square root of 45 is approximately 6.708.
Alternatively, you can use a calculator to find the square root of 45, which will give you an exact value of approximately 6.708203932499369.