Answer :
To determine the value of [tex]\(\sqrt{\frac{\sqrt{3}-1}{\sqrt{3}+1}}\)[/tex] given that [tex]\(\sqrt{3} = 1.732\)[/tex], follow these steps:
1. Calculate the Numerator [tex]\(\sqrt{3} - 1\)[/tex]:
[tex]\[ \sqrt{3} = 1.732 \][/tex]
[tex]\[ \sqrt{3} - 1 = 1.732 - 1 = 0.732 \][/tex]
2. Calculate the Denominator [tex]\(\sqrt{3} + 1\)[/tex]:
[tex]\[ \sqrt{3} = 1.732 \][/tex]
[tex]\[ \sqrt{3} + 1 = 1.732 + 1 = 2.732 \][/tex]
3. Form the Fraction [tex]\(\frac{\sqrt{3} - 1}{\sqrt{3} + 1}\)[/tex]:
[tex]\[ \frac{\sqrt{3} - 1}{\sqrt{3} + 1} = \frac{0.732}{2.732} \approx 0.2679355783308931 \][/tex]
4. Calculate the Square Root of the Fraction:
[tex]\[ \sqrt{0.2679355783308931} \approx 0.5176249398269881 \][/tex]
So, the value of [tex]\(\sqrt{\frac{\sqrt{3}-1}{\sqrt{3}+1}} \approx 0.5176\)[/tex].
Therefore, the correct answer is:
(d) 0.517
1. Calculate the Numerator [tex]\(\sqrt{3} - 1\)[/tex]:
[tex]\[ \sqrt{3} = 1.732 \][/tex]
[tex]\[ \sqrt{3} - 1 = 1.732 - 1 = 0.732 \][/tex]
2. Calculate the Denominator [tex]\(\sqrt{3} + 1\)[/tex]:
[tex]\[ \sqrt{3} = 1.732 \][/tex]
[tex]\[ \sqrt{3} + 1 = 1.732 + 1 = 2.732 \][/tex]
3. Form the Fraction [tex]\(\frac{\sqrt{3} - 1}{\sqrt{3} + 1}\)[/tex]:
[tex]\[ \frac{\sqrt{3} - 1}{\sqrt{3} + 1} = \frac{0.732}{2.732} \approx 0.2679355783308931 \][/tex]
4. Calculate the Square Root of the Fraction:
[tex]\[ \sqrt{0.2679355783308931} \approx 0.5176249398269881 \][/tex]
So, the value of [tex]\(\sqrt{\frac{\sqrt{3}-1}{\sqrt{3}+1}} \approx 0.5176\)[/tex].
Therefore, the correct answer is:
(d) 0.517
