Week 3 Absolute Value and Simplifying Radical Expressions

This week in Pre Calculus 11, we learned what an absolute value of a real number was and how to simplify radical expressions.

Absolute Value of a Real Number : The principal square root of a square number. 

SOLUTION: The absolute value of a negative number is the opposite number, and the absolute value of a positive number and 0 are the same.

ex/    |-99| = 99         | 12 | = 12

This is because distance is always positive.

 

The long lines act as brackets but are not and it represents absolute value.

  • ex 1/         4 |15-20|
  •                     4 |-5|
  •                     4 (5)
  •                     = 20

 

  • ex 2/         |6 +(-10)| -|5-7|
  •                     |6-10| – | -2|
  •                     |-4| – |2|
  •                     4  –   2
  •                     = 2

 

Here is a video that really helped me learn and understand a little bit more about absolute value.

 

Radical Expressions

we also briefly reviewed radical expressions

Here a link to another post for radical expressions : http://myriverside.sd43.bc.ca/jessicap2015/2017/02/11/math-10-week-2/

ex/ \sqrt{25} =   5  and 3\sqrt[2]{5} = \sqrt{45}

 

Now to build off of radical expressions we are adding variables.

Solving

Step 1: Find perfect squares.

Step 2: Take them out / simplify

Step 3: Do the same with the variables (treat them like numbers)

ex/ \sqrt[2]{18x}

  • ex/ \sqrt[2]{18x^2}
  • \sqrt{9\cdot{x^2}\cdot2}
  • \sqrt{3\cdot3\cdot{x}\cdot{x}\cdot2}
  • 3x\sqrt[2]{2}

 

 

This is how to work with variables in Radical Expressions

 

 

 

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