i) Let's start by finding the value of [tex]\(\sqrt{3}\)[/tex] to one decimal place.
1. Value of [tex]\(\sqrt{3}\)[/tex] to one decimal place:
The value of [tex]\(\sqrt{3}\)[/tex] rounded to one decimal place is approximately [tex]\(1.7\)[/tex].
2. Calculate the expression [tex]\(\frac{3 - \sqrt{3}}{3 + \sqrt{3}}\)[/tex]:
Substitute [tex]\(\sqrt{3} = 1.7\)[/tex] into the expression:
[tex]\[
\frac{3 - 1.7}{3 + 1.7}
\][/tex]
Simplify the numerator and denominator:
[tex]\[
\frac{1.3}{4.7}
\][/tex]
The value of [tex]\(\frac{1.3}{4.7}\)[/tex] is approximately [tex]\(0.2765957446808511\)[/tex].
3. Find the square root of the result [tex]\(\frac{1.3}{4.7}\)[/tex]:
Now, we need to find the square root of the decimal result [tex]\(0.2765957446808511\)[/tex]:
[tex]\[
\sqrt{0.2765957446808511}
\][/tex]
The square root of [tex]\(0.2765957446808511\)[/tex] is approximately [tex]\(0.5259237061407777\)[/tex].
Summary of Results:
- [tex]\(\sqrt{3} \approx 1.7\)[/tex]
- [tex]\(\frac{3 - \sqrt{3}}{3 + \sqrt{3}} \approx \frac{1.3}{4.7} \approx 0.2765957446808511\)[/tex]
- [tex]\(\sqrt{0.2765957446808511} \approx 0.5259237061407777\)[/tex]
Therefore, the value of [tex]\(\sqrt{3}\)[/tex] to one decimal place is [tex]\(1.7\)[/tex], and the square root of [tex]\(\frac{3 - \sqrt{3}}{3 + \sqrt{3}}\)[/tex] is approximately [tex]\(0.5259237061407777\)[/tex].
