WORKING WITH RADICALS

Hey everbody, my name is Adam and I will be your scribe today.

Today in class we learned about Radicals, specifically about converting mixed radicals into entire radicals and vice versa, and adding and subtracting radicals.

CONVERTING MIXED RADICALS INTO ENTIRE RADICALS

Let's start with an example from our booklet.

To solve this, first we write the coefficient as a cube root and make it to the power of three. (Because of the index)

Now cube both values from .

Combine both terms by adding them together to get the final answer.

EXPRESSING ENTIRE RADICALS AS MIXED RADICALS

To solve this problem below, we can solve this problem using Greatest Perfect Square Factor, and by Prime Factorization.

First, we have to separate the radical by finding the Greatest Perfect Square Factor or by Prime Factorization for the integer and by separating the variable.

For finding the Greatest Perfect Square Factor of that integer, we have to list the factors of that number and find the highest perfect square.

The factors of are:

The highest perfect square is so the equation will be:

Which will reduce into:

For Prime Factorization, we find the prime factors by doing a factor tree.

Now if we square root all the pairs, it will end up like this:

Which will end up the same as the above equation:

To separate the variables from the radicals, we have to separate the variables in pairs. (because it is a square root) and simplify the equation.

To get the final answer, we just combine the into .

ADDING AND SUBTRACTING RADICALS

To solve this problem below, we have to note that you can only add or subtract like radicals and those are radicals with the same radicand.

First, we have convert every radical into a mixed radical.

Note that can be reduced because (a perfect square) is a factor of .

Now, combine all the like radicals to get your final answer.

Hope this blog helped you out, just don't ask me about it tomorrow.

And finally . . .

***GO BOMBERS!***