During this week I learnt how to properly add and subtract radicals. I chose to share my understanding of this subject because I believe that it is important to know the basics before jumping into more complicated equations, knowing how to add and subtract radicals very proficiently will be beneficial for this math unit because it is a foundation block for more complicated equations to come.
If the radicals that you are adding or subtracting share the same radicand and index, then you can add and subtract the coefficients whilst keeping the radicand and index the same. If the radicals are more complicated and don’t share the same radicand than simplify if you can by turning it into a mixed radical! If you still can’t get the same radicands or the index is different then leave the simplified components as your answer.
Question 1- Displays the perfect example of adding and subtracting radicals that already have been simplified and has similar radicands and index’s. The 4 components of this equation either have a radicand of 2 or 5. Knowing that we don’t need to simplify and that we can identify the similar square roots and radicands, we can now add or subtract like terms. Such as subtracting square root 2 coefficient 5 with square root 2 coefficient negative 3.
Question 2- Needs to be simplified before we start adding or subtracting coefficients. To simplify the mixed radical create a factor tree. The factor tree of 63 is 9 and 7, 9 being a perfect square, is removed from the radicand and is multiplied with the coefficient and we keep the non-perfect roots like 7 in the radicand. We go through the same process with 28 and now we have the common radicand of 7 so we are now ready to subtract the coefficients.
