Simplify [tex]$\frac{544^2-6}{34+1}$[/tex]
Answer (2)
To simplify 34 + 1 54 4 2 − 6 , first calculate the square of 544, subtract 6, and then divide by 35. This results in approximately 8455.14 .
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Simplify the denominator: 34 + 1 = 35 .
Calculate the square: 54 4 2 = 295936 .
Subtract 6 from the square: 295936 − 6 = 295930 .
Divide the result by the denominator: 35 295930 = 8455.142857142857 . Therefore, the simplified expression is approximately 8455.14 .
Explanation
Understanding the Problem We are asked to simplify the expression 34 + 1 54 4 2 − 6 . This involves evaluating the square of 544, subtracting 6 from it, and then dividing the result by the sum of 34 and 1.
Simplifying the Denominator First, we simplify the denominator: 34 + 1 = 35
Calculating the Square Next, we calculate 54 4 2 : 54 4 2 = 544 × 544 = 295936
Subtracting 6 Now, we subtract 6 from the result: 295936 − 6 = 295930
Dividing to Get the Final Answer Finally, we divide the result by the simplified denominator: 35 295930 = 8455.142857142857 Rounding to two decimal places, we get 8455.14.
Examples
Understanding how to simplify expressions like this is useful in many real-world situations. For example, if you're calculating the area of a square with side length 544 and then need to adjust it by a small amount, you might encounter a similar calculation. Also, in computer programming, simplifying expressions is crucial for optimizing code and making it run faster. This skill is also helpful in financial calculations, such as determining the value of an investment after a certain period.
