Estimate √53 between two numbers to the tenths place.

Question

1. Identify perfect squares: 72 = 49 and 82 = 64
2. Estimate between two whole numbers: between 7 and 8
3. Determine the closer whole number: closer to 7 because 53 is closer to 49 than to 64
4. Find the squares of tenths: 7.12= 50.41
7.22= 51.84
7.32= 53.29
7.42= 54.76
√53 lies between
and
.

Answer 1

To estimate √53 to the tenths place, we can follow the steps you've outlined.

1. Identify perfect squares:
   We note that \(7^2 = 49\) and \(8^2 = 64\), so \(√53\) is between 7 and 8.

2. Estimate between two whole numbers:
   Since \(49 < 53 < 64\), we confirm that \(√53\) lies between 7 and 8.

3. Determine the closer whole number:
   Since \(53\) is closer to \(49\) than to \(64\), \(√53\) is closer to \(7\).

4. Find the squares of tenths:

   • \(7.1^2 = 50.41\)
   • \(7.2^2 = 51.84\)
   • \(7.3^2 = 53.29\) (this is more than 53)
   • \(7.4^2 = 54.76\)

Putting this together, we find that \(√53\) lies between \(7.2\) (which gives us \(51.84\)) and \(7.3\) (which gives us \(53.29\)).

Thus, the estimate can be concluded as:

√53 lies between 7.2 and 7.3.