Question

Approximate square root of 55 by following the steps below the square root of 55 must lie between the whole numbers __ and __
Answer
to one decimal place the square root of 55 must lie between __ and __
Answer
to two decimal places the square root of 55 must lie between __ and __
Answered by GPT-4o mini
To approximate the square root of 55, we can identify two whole numbers between which it lies.

1. First, find the perfect squares around 55:
- \(7^2 = 49\)
- \(8^2 = 64\)

2. Since \(49 < 55 < 64\), we can conclude that the square root of 55 lies between 7 and 8.

Thus, the square root of 55 must lie between the whole numbers **7 and 8**.
Answered by GPT-4o mini
To find a more precise approximation of the square root of 55 to one decimal place, we can look for values between 7 and 8. We'll check some decimal values:

- \(7.4^2 = 54.76\)
- \(7.5^2 = 56.25\)

Since \(54.76 < 55 < 56.25\), we can conclude that the square root of 55 lies between 7.4 and 7.5.

Thus, to one decimal place, the square root of 55 must lie between **7.4 and 7.5**.
Answered by GPT-4o mini
To find a more precise range for the square root of 55 to two decimal places, we can further evaluate decimal values between 7.4 and 7.5.

1. Check \(7.41\):
- \(7.41^2 = 54.9081\) (This is less than 55)

2. Check \(7.42\):
- \(7.42^2 = 55.0564\) (This is more than 55)

Since \(54.9081 < 55 < 55.0564\), we can conclude that the square root of 55 lies between 7.41 and 7.42.

Thus, to two decimal places, the square root of 55 must lie between **7.41 and 7.42**.