After doing the chapter 1 test, we started looking at Absolute value and Radical expressions.

Absolute value is a simple concept which just means ‘the distance from zero’. For example, the number 6 is 6 places away from zero. Therefore, the absolute value of 6 is just 6.

The absolute value of a number can be shown like this:

|6| = 6

Likewise, the absolute value of -6 is also 6 because it is 6 places away from zero. |-6| = 6

The absolute value can be applied to any number: |-243| = 243,      |-0.35| = 0.35,      |-102938475| = 102938475  etc…

 

The next day we learned about simplifying Radical expressions:

A radical expression is just a number that is under a square root or a cube root. Like . This would equal 8 because (8×8)=64.

Sometimes, these radicals can be a number like . This is not a perfect square so we are unable to answer with a natural number. However, we can further reduce it and turn it into a mixed radical. This can take on the form of 3. This just means that there is a coefficient in front of the root sign.

We can further simplify  to the mixed form of 5

We obtain this number by doing the following steps:

Here we have taken out all the factors of 250 using a factor tree and we group the two fives together and bring them outside of the square root sign. 5 and 2 cannot be further simplified so we just leave them be as 10.

 

This brings us to our final answer in mixed form: 5. We learn how to convert into a mixed radical so that we can later multiply and divide these radical expressions.