To determine which of the following numbers is between 5 and 7, we need to evaluate each option and see if it lies within that range:
A. [tex]\(\sqrt{6}\)[/tex]
B. [tex]\(\sqrt{35}\)[/tex]
C. [tex]\(\sqrt[3]{27}\)[/tex]
Let's evaluate each option:
1. Option A: [tex]\(\sqrt{6}\)[/tex]
Calculate the square root of 6.
[tex]\[
\sqrt{6} \approx 2.449
\][/tex]
This value, approximately 2.449, is less than 5. Therefore, [tex]\(\sqrt{6}\)[/tex] is not between 5 and 7.
2. Option B: [tex]\(\sqrt{35}\)[/tex]
Calculate the square root of 35.
[tex]\[
\sqrt{35} \approx 5.916
\][/tex]
This value, approximately 5.916, falls within the range of 5 and 7. Therefore, [tex]\(\sqrt{35}\)[/tex] is between 5 and 7.
3. Option C: [tex]\(\sqrt[3]{27}\)[/tex]
Calculate the cube root of 27.
[tex]\[
\sqrt[3]{27} = 3
\][/tex]
This value is exactly 3, which is less than 5. Therefore, [tex]\(\sqrt[3]{27}\)[/tex] is not between 5 and 7.
In summary, by evaluating each option, we find that the only number between 5 and 7 is:
[tex]\[
\boxed{\sqrt{35}}
\][/tex]
