Use a calculator to find the result of the following operations with five decimal places of approximation.
a) [tex]$\sqrt{3}+\sqrt{5}$[/tex]
b) [tex]$\sqrt{7}(\pi-\sqrt{5})$[/tex]
c) [tex]$\pi(2-3 \pi-\sqrt{11})$[/tex]
Answer (1)
The problem requires calculating three expressions and rounding the results to five decimal places.
Calculate 3 + 5 and round to five decimal places: 3.96812 .
Calculate 7 ( π − 5 ) and round to five decimal places: 2.39579 .
Calculate π ( 2 − 3 π − 11 ) and round to five decimal places: − 33.74511 .
The final answers are: 3.96812 , 2.39579 , − 33.74511 .
Explanation
Problem Analysis We are asked to use a calculator to find the result of the following operations with five decimal places of approximation: a) 3 + 5 b) 7 ( π − 5 ) c) π ( 2 − 3 π − 11 )
Calculations a) 3 + 5 ≈ 3.968118785068667 . Rounding to five decimal places, we get 3.96812 .
b) 7 ( π − 5 ) ≈ 2.395793098966465 . Rounding to five decimal places, we get 2.39579 .
c) π ( 2 − 3 π − 11 ) ≈ − 33.7451119721828 . Rounding to five decimal places, we get − 33.74511 .
Final Answer Therefore, the results of the operations, rounded to five decimal places, are: a) 3.96812 b) 2.39579 c) − 33.74511
Examples
In physics, when calculating the magnitude of a resultant vector that involves square roots and constants like pi, these calculations are essential. For instance, determining the net force acting on an object might require summing vectors with components involving such expressions. Accurate approximations, like rounding to five decimal places, ensure the precision needed for reliable predictions and analyses in various scientific and engineering applications.
