To estimate the square root of 3 to two decimal places, let's consider the value of the square root of 3 and round it accordingly.
Firstly, we know that the square root of 3 is a bit less than 2 because [tex]\(2^2 = 4\)[/tex] and [tex]\(1^2 = 1\)[/tex]. Therefore, [tex]\(\sqrt{3}\)[/tex] is between 1 and 2.
To get a finer estimate, we can look at numbers closer to 3. For instance, [tex]\(1.7^2 = 2.89\)[/tex] and [tex]\(1.8^2 = 3.24\)[/tex]. Since [tex]\(2.89 < 3 < 3.24\)[/tex], we can see that [tex]\(\sqrt{3}\)[/tex] is between 1.7 and 1.8.
To narrow it down further, we can say:
[tex]\[
1.73 \approx \sqrt{3}
\][/tex]
Rounding to two decimal places, we get:
[tex]\[
\sqrt{3} \approx 1.73
\][/tex]
So, we conclude that:
[tex]\[
\sqrt{3} \approx 1.73
\][/tex]
