Estimate [tex]\(\sqrt{50}\)[/tex] to the hundredths place.

1. Estimate between two whole numbers:
[tex]\(7^2 = 49, \quad 8^2 = 64\)[/tex]

2. Estimate further to the tenths place:
[tex]\(7.0^2 = 49.0, \quad 7.1^2 = 50.41\)[/tex]

3. Estimate further to the hundredths place:

The [tex]\(\sqrt{50}\)[/tex] is between [tex]\(7.04\)[/tex] and [tex]\(\square\)[/tex].



Answer :

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].