To estimate [tex]\(\sqrt{50}\)[/tex] to the hundredths place, we can follow the steps below:
1. Estimate between two whole numbers:
[tex]\[
7^2 = 49 \quad \text{and} \quad 8^2 = 64
\][/tex]
Since [tex]\(49 < 50 < 64\)[/tex], [tex]\(\sqrt{50}\)[/tex] is between [tex]\(7\)[/tex] and [tex]\(8\)[/tex].
2. Estimate further to the tenths place:
[tex]\[
7.0^2 = 49.0 \quad \text{and} \quad 7.1^2 \approx 50.41
\][/tex]
Since [tex]\(7.0^2 = 49.0\)[/tex] is less than [tex]\(50\)[/tex] and [tex]\(7.1^2 \approx 50.41\)[/tex] is slightly greater than [tex]\(50\)[/tex], [tex]\(\sqrt{50}\)[/tex] is between [tex]\(7.0\)[/tex] and [tex]\(7.1\)[/tex].
3. Estimate further to the hundredths place:
[tex]\[
7.04^2 \approx 49.4016 \quad \text{and} \quad 7.05^2 \approx 49.5025
\][/tex]
Since [tex]\(49.4016 < 50 < 49.5025\)[/tex], we can refine our estimate to conclude that [tex]\(\sqrt{50}\)[/tex] is indeed between [tex]\(7.04\)[/tex] and [tex]\(7.05\)[/tex].
Therefore, [tex]\(\sqrt{50}\)[/tex] is estimated to be between [tex]\(7.04\)[/tex] and [tex]\(7.05\)[/tex].
