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zorro
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Homework Statement
I got this expression while solving a problem.
sin(theta)=[√3+1-√(4-2√3)]/4
Using calculator I got RHS=0.5
How do we simplify it without using a calc?
ehild said:Naturally, √3 +a = 1.7320508.. +a. You have to perform a higher operation first, and square root is of higher order than addition or subtraction. So is multiplication to addition. 2*3+4 =10 and it is not the same as 2*(3+4)=14. Or 6/2+3=6, and not 6/(2+3)=1.2. √9+16=19 and it is not √(9+16)=5. The square of (√3-1) is (√3-1)^2 = 4-2√3 and not √3-1^2=√3-1. Or it is on the other way at other parts of the world?
ehild
Radical simplification is the process of reducing complex systems or ideas into their most basic and essential components. It involves removing unnecessary complexities and focusing on the core elements.
Radical simplification allows for easier understanding and communication of complex concepts. It can also lead to increased efficiency and effectiveness in problem-solving and decision-making.
In scientific research, radical simplification can be used to break down complex theories or experiments into simpler components, making it easier to understand and analyze the results. It can also help to identify key variables and relationships between them.
One potential challenge is oversimplification, where important details or nuances are overlooked. Another challenge is resistance to change, as some may be hesitant to adopt a more simplified approach.
Yes, radical simplification can be applied to any area of science, from biology to physics to psychology. It is a universal concept that can help in understanding and advancing knowledge in any field.