Solving a Complex Mathematical Expression
The image shows a mathematical expression that needs solving. The expression is written as:
(2⅔)² ÷ √(16) + 4.02 / √(16 / 64)
Let's solve this step-by-step:
1. Calculate the square of 2⅔:
- Convert the mixed number to an improper fraction: \(2 \frac{2}{3} = \frac{8}{3}\).
- Square the fraction: \(\left(\frac{8}{3}\right)^2 = \frac{64}{9}\).
2. Divide the squared fraction by the square root of 16:
- The square root of 16 is 4.
- Divide the fraction by 4: \(\frac{64}{9} \div 4 = \frac{64}{9} \times \frac{1}{4} = \frac{64}{36} = \frac{16}{9}\).
3. Calculate the division on the right side of the plus sign:
- The square root of (16/64) is the square root of 0.25, which is 0.5.
- Perform the division 4.02 / 0.5: \(4.02 \div 0.5 = 8.04\).
4. Sum the two results:
- Transform \(\frac{16}{9}\) into decimal: \( \frac{16}{9} \approx 1.777... \).
- Add this value to 8.04: \( 1.777 + 8.04 = 9.817...\).
So, the result of the given expression is approximately 9.817.
Please note that the square root symbol applies to the number immediately following it, so in each case, I calculated the square root of that number before performing the further operations. If the intention of the expression was for the square root to apply to more than just the number immediately following it, then the expression would need to be written with clear grouping symbols, such as parentheses, to indicate this.
