Applying terms in square roots -yeesh

In summary, square roots are a mathematical concept used to simplify equations and solve for unknown variables. They involve finding the number that, when multiplied by itself, gives the original number. Square roots can be applied to negative numbers, resulting in complex numbers using the imaginary number "i". They can be calculated using a calculator or manually using the square root algorithm. Special rules for applying square roots include only taking out perfect square factors and simplifying expressions by multiplying the numbers under the square roots. In real-life, square roots are commonly used in fields such as engineering, physics, and finance, as well as in everyday situations such as calculating dimensions or finding lengths.
  • #1
Parabox
10
0
http://img522.imageshack.us/img522/7522/mat4vj.gif where X is the number into the term http://img524.imageshack.us/img524/2985/prob23ei.gif
Computer F'(6)

The square root is what's giving me my most difficulty. I don't know how to apply the term with a square root and computer f'(6). I've about given up, but it's important to know. Help is needed for this one.
 
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  • #2
Do you know the chain rule?

Think of the general case where [itex]f(x) = \sqrt{ax + b} = (ax+b)^{0.5}[/itex]. Now let u=ax+b and apply the chain rule.
 

1. What are square roots and how are they applied?

Square roots are a mathematical concept that represents the number that, when multiplied by itself, gives the original number. To apply square roots, we take the square root of a given number and use it to simplify complex equations or solve for unknown variables.

2. Can square roots be applied to negative numbers?

Yes, square roots can be applied to negative numbers. However, the result will be a complex number, since a negative number multiplied by itself results in a positive number. In these cases, we use the imaginary number "i" to represent the square root of a negative number.

3. How do we calculate square roots?

To calculate square roots, we can use a calculator or perform the calculation manually using the square root algorithm. This involves repeatedly finding the square root of a number until we reach a desired level of accuracy.

4. Are there any special rules for applying square roots?

Yes, there are a few special rules for applying square roots. For example, when simplifying square roots, we can only take out numbers that have a perfect square factor. Additionally, when multiplying two numbers with square roots, we can simplify the expression by multiplying the numbers under the square roots together.

5. How are square roots applied in real-life situations?

Square roots are commonly used in fields such as engineering, physics, and finance to solve complex equations and problems. They can also be used in everyday situations, such as calculating the dimensions of a room or finding the length of a diagonal line in a square or rectangle.

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