Certainly! Let's break down the given expression step-by-step:
The expression is:
[tex]\[ \sqrt{\sqrt{1}} + \sqrt{9 \cdot 16} + \left(\frac{1}{3}\right)^{-1} + 2^0 \][/tex]
1. Evaluate the first term: [tex]\(\sqrt{\sqrt{1}}\)[/tex]
- We start with the innermost square root: [tex]\(\sqrt{1} = 1\)[/tex].
- Then, we take the square root of the result: [tex]\(\sqrt{1} = 1\)[/tex].
Therefore, the first term is:
[tex]\[ \sqrt{\sqrt{1}} = 1.0 \][/tex]
2. Evaluate the second term: [tex]\(\sqrt{9 \cdot 16}\)[/tex]
- First, we multiply the numbers inside the square root: [tex]\(9 \cdot 16 = 144\)[/tex].
- Then, we take the square root of the product: [tex]\(\sqrt{144} = 12\)[/tex].
Therefore, the second term is:
[tex]\[ \sqrt{9 \cdot 16} = 12.0 \][/tex]
3. Evaluate the third term: [tex]\(\left(\frac{1}{3}\right)^{-1}\)[/tex]
- The expression [tex]\(\left(\frac{1}{3}\right)^{-1}\)[/tex] is equivalent to taking the reciprocal of [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ \left(\frac{1}{3}\right)^{-1} = \frac{1}{\left(\frac{1}{3}\right)} = 3 \][/tex]
Therefore, the third term is:
[tex]\[ \left(\frac{1}{3}\right)^{-1} = 3.0 \][/tex]
4. Evaluate the fourth term: [tex]\(2^0\)[/tex]
- We know that any number raised to the power of 0 is 1:
[tex]\[ 2^0 = 1 \][/tex]
Therefore, the fourth term is:
[tex]\[ 2^0 = 1.0 \][/tex]
5. Sum all the terms to get the final result
Now, we add all the terms together:
[tex]\[ 1.0 + 12.0 + 3.0 + 1.0 = 17.0 \][/tex]
Thus, the final result of the given expression is:
[tex]\[ \boxed{17.0} \][/tex]
