Macivitament
1) $\frac{1}{\sqrt{3}}$
Answer (1)
The problem asks to simplify 3 1 .
Rationalize the denominator by multiplying both the numerator and the denominator by 3 .
The rationalized form is 3 3 .
The final answer is 3 3 .
Explanation
Understanding the Problem The problem presents the expression 3 1 and asks to perform 'Macivitament'. Since the instruction is not clear, I will assume that the task is to rationalize the denominator of the given expression.
Rationalizing the Denominator To rationalize the denominator, I need to multiply both the numerator and the denominator by 3 . This will eliminate the square root from the denominator.
Performing the Calculation Multiplying the numerator and denominator by 3 , we get: 3 1 × 3 3 = 3 3 Thus, the rationalized form of the expression is 3 3 .
Final Answer The decimal value of the expression 3 1 is approximately 0.577. The rationalized form of the expression is 3 3 .
Examples
Rationalizing the denominator is a useful skill in various mathematical contexts. For example, when dealing with trigonometric functions or simplifying complex expressions, it's often necessary to remove square roots from the denominator to make further calculations easier. Imagine you are calculating the impedance in an electrical circuit and one of your intermediate results is 2 1 . Rationalizing this to 2 2 can simplify subsequent calculations and make the final result easier to interpret. This technique ensures that expressions are in their simplest and most manageable form.
