Day: February 17, 2018

Week 3 – Absolute Value & Radicals

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This week in Pre-Calc 11 we started the Absolute Value and Radicals unit. We learned the basics about absolute value and reviewed simplifying radicals.

What is the Absolute Value of a Real Number? The absolute value of a real number is the principle square root of the square of a number.

Sign: \mid\mid 

The absolute value of a number is it’s distance away from 0. The absolute value of a number is always positive.

Ex. 1 \mid-10\mid=10

Ex. 2 \mid10\mid=10

In the examples above I showed the absolute value of a positive and negative number. -10 and 10 have the same absolute value because they are the same distance away from 0; both numbers are 10 spaces away from 0.

How do you simplify an expression? The \mid\mid act like brackets. You simplify everything inside the absolute value sign and then move to the outside.

Ex. 9\mid3+6(-6)\mid

9\mid3-36\mid

9\mid-33\mid 

9(33) 

297

In the example above, I solved everything inside the absolute value symbol. Then, I figured out the absolute value -33 which is 33. Lastly, I multiplied the absolute value by the number outside of the absolute value symbol.

How to Simplify Radicals: To simplify radicals you have to break the radicand down by using perfect squares.

Ex. \sqrt18 

\sqrt9*2

\sqrt9\times\sqrt2

3\sqrt2 

In the example I broke down the square root of 18 by using the number 9. 9 can divide into 18 and is a perfect square. After I figured out that 9*2=18 I removed 9 from inside the radical by finding the square root of 9 and moving it to the outside.