Answer :
The correct option is [tex]\(\boxed{\text{a. } 6^{1/6}}\)[/tex].
To find the square root of the cube root of 6, we first calculate the cube root of 6, then find the square root of that result.
1. Cube root of 6: [tex]\( \sqrt[3]{6} \)[/tex]
2. Square root of the result obtained from step 1: [tex]\( \sqrt{\sqrt[3]{6}} \)[/tex]
We can simplify this expression as follows:
[tex]\[ \sqrt{\sqrt[3]{6}} = (6^{1/3})^{1/2} = 6^{1/3 \times 1/2} = 6^{1/6} \][/tex]
Therefore, the square root of the cube root of 6 is \(6^{1/6}\).
Among the given options:
a. [tex]\(6^{1/6}\)[/tex]
b. [tex]\(6^{1/3}\)[/tex]
c. [tex]\(6^{2/3}\)[/tex]
d. [tex]\(6^{3/2}\)[/tex]
The correct option is [tex]\(\boxed{\text{a. } 6^{1/6}}\)[/tex].
The complete Question is given below:
Which of the following is equal to the square root of the cube root of 6 ? (1 point)
a. 6 to the power of 1 over 6
b. 6 to the power of 1 over 3
c. 6 to the power of 2 over 3
d. 6 to the power of 3 over 2
