Simplifying surds as numerators

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In summary, the conversation is about simplifying fractions with surds. The original expression is split into two fractions, with one containing a square root. The process involves eliminating roots from denominators and evaluating the negative signs.
  • #1
MattVonFat
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Hi,

I was reading about surds and saw this:

[PLAIN]http://www.mattvonfat.com/eq.png

I'm probably not as familiar with simplifying fractions as I should be but I think I get that it's being split into two fractions and that √3/2 is the same as 1/2*√3 but I don't understand what's actually being done to √3/2 to simplify it and why the original expression isn't left as it is.

Any help would be much appreciated!

Thanks,
Matt
 
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  • #2
Nothing wrong with either form of the expression.
Usually we eliminate roots from denominators.
Numerators with roots are fine.
 
  • #3
it might help to think of it like this:

2/3 - 1/3 = (2-1)/3

So reverse would be the same:

(2-1)/3 = 2/3 - 1/3

if 3 were negative, then the negatives would evaluate:

(2-1)/-3 = 2/-3 - 1/-3 = -2/3 - (-1/3) = -2/3 + 1/3
 

What is the purpose of simplifying surds as numerators?

The purpose of simplifying surds as numerators is to make mathematical expressions and equations easier to work with. It also allows for a clearer understanding of the underlying concepts and principles involved.

How do you simplify surds as numerators?

To simplify surds as numerators, you need to factor out the largest perfect square from the surd. Then, you can simplify the remaining surd by applying the appropriate mathematical operations (e.g. addition, subtraction, multiplication) to the coefficients and the surd itself.

Why is it important to simplify surds as numerators?

Simplifying surds as numerators is important because it helps to reduce the complexity of mathematical expressions and equations. It also allows for easier manipulation and calculation of these expressions, which can be useful in solving problems and arriving at solutions.

What are the common mistakes to avoid when simplifying surds as numerators?

One of the most common mistakes to avoid when simplifying surds as numerators is not properly identifying and factoring out the largest perfect square from the surd. Another mistake is not simplifying the coefficients and the surd separately before combining them again.

What are some real-world applications of simplifying surds as numerators?

Simplifying surds as numerators is used in various fields such as engineering, physics, and finance. For example, in engineering, it is used to simplify complex equations involving square roots in order to solve problems related to electricity, mechanics, and thermodynamics. In finance, it is used to calculate interest rates and compound growth, which involves surds and their simplification.

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