Let's solve the expression [tex]\(\sqrt[6]{\sqrt[2]{256}}\)[/tex] step by step.
### Step 1: Calculate [tex]\(\sqrt[2]{256}\)[/tex]
First, we need to find the square root of 256. The square root of 256 is 16, as [tex]\(16 \times 16 = 256\)[/tex]. So:
[tex]\[ \sqrt[2]{256} = 16 \][/tex]
### Step 2: Calculate [tex]\(\sqrt[6]{16}\)[/tex]
Next, we need to find the sixth root of 16. The sixth root of a number is the number that, when raised to the power of 6, gives the original number.
The sixth root of 16 is approximately 1.5874 (up to four decimal places), since:
[tex]\[ 1.5874^6 \approx 16 \][/tex]
So,
[tex]\[ \sqrt[6]{16} \approx 1.5874 \][/tex]
### Final Result
Therefore, [tex]\(\sqrt[6]{\sqrt[2]{256}}\)[/tex] simplifies to approximately 1.5874.
