Sure, let's work through the solution step by step.
1. Convert the Mixed Number:
Firstly, we need to convert the mixed number [tex]\( 3 \frac{1}{3} \)[/tex] into an improper fraction or a decimal.
- A mixed number [tex]\( 3 \frac{1}{3} \)[/tex] is the same as [tex]\( 3 + \frac{1}{3} \)[/tex].
- Converting [tex]\( \frac{1}{3} \)[/tex] to a decimal, we get approximately [tex]\( 0.3333\ldots \)[/tex] (repeating decimal).
- So, [tex]\( 3 + \frac{1}{3} \approx 3.3333\ldots \)[/tex].
2. Simplify the Square Root:
Next, we need to evaluate the square root of 52.
- When [tex]\( \sqrt{52} \)[/tex] is simplified, we get approximately [tex]\( 7.2111 \)[/tex].
3. Multiplication:
Now, we multiply the decimal representation of the mixed number with the square root of 52.
- Using the approximate values, we multiply:
[tex]\[ 3.3333\ldots \times 7.2111 \approx 24.037 \][/tex]
So, the final result of multiplying the mixed number [tex]\( 3 \frac{1}{3} \)[/tex] by [tex]\( \sqrt{52} \)[/tex] is approximately [tex]\( 24.037 \)[/tex], accurate to three decimal places.
Therefore, the completed expression:
[tex]\[ 3 \frac{1}{3} \times \sqrt{52} \approx 24.037 \][/tex]
