To find the value of [tex]\(\frac{\sqrt{7} + \sqrt{2}}{\sqrt{3}}\)[/tex] correct to 4 decimal places, follow these steps:
1. Evaluate the square roots in the numerator:
- Calculate [tex]\(\sqrt{7}\)[/tex].
- Calculate [tex]\(\sqrt{2}\)[/tex].
2. Sum the square roots:
- Add the values of [tex]\(\sqrt{7}\)[/tex] and [tex]\(\sqrt{2}\)[/tex].
3. Evaluate the square root in the denominator:
- Calculate [tex]\(\sqrt{3}\)[/tex].
4. Perform the division:
- Divide the sum of the square roots by [tex]\(\sqrt{3}\)[/tex].
5. Round the result:
- Round the division result to 4 decimal places.
Following these steps:
1. The evaluated values are:
- [tex]\(\sqrt{7} \approx 2.6458\)[/tex]
- [tex]\(\sqrt{2} \approx 1.4142\)[/tex]
2. Sum the square roots:
[tex]\[
2.6458 + 1.4142 = 4.0600
\][/tex]
3. The evaluated value is:
- [tex]\(\sqrt{3} \approx 1.7321\)[/tex]
4. Perform the division:
[tex]\[
\frac{4.0600}{1.7321} \approx 2.3440
\][/tex]
5. Round the result to 4 decimal places:
[tex]\[
2.3440 \approx 2.344
\][/tex]
Thus, the value of [tex]\(\frac{\sqrt{7} + \sqrt{2}}{\sqrt{3}}\)[/tex] correct to 4 decimal places is:
[tex]\[
2.344
\][/tex]
