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 $\surd 53$ is between 7 and 8.

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

3. Determine the closer whole number:
   Since $53$ is closer to $49$ than to $64$, $\surd 53$ 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 $\surd 53$ 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.