Adding and Subtracting Radical Expressions - Problem 3

Here this looks like it’s going to be a really challenging problem because not only do I have different radicands in each one of my terms, but also they involve x and regular old numbers that probably need to be simplified. So it’s going to be lots of steps. What I’m, going to do is just simplify each one of these one at a time looking to see if they have the same radicands and then combine them at the end.

Okay so first let’s simplify square root of 125x. I want to look for products that equal 125 where one of my factors is a perfect square. Well for me I was thinking of 25 times 5 times square root of x. That’s simplified into the product of its factors. Well square root of 25 you guys know is just regular 5, and then I have square root of 5x left. Okay that’s my first term simplified. Let’s look at the second one.

4 times square root of 20x, well the 4 is going to stay square root of 20x I want to look for factors that involve a perfect square like I’m going to use 4 and 5. Square root of 4 times square root of 5 times square root of x. That’s cools because square root of 4 is 2, so really what I have is 4 times 2 which is 8 square roots of 5x. Sweet I’m on my way because these first two times already have the same radicands I moved to that plus sign down from there.

Okay now I’m going to work with this guy. I need 3 times 2 numbers that multiply to 45 hopefully one of them can be a perfect square. Well things I multiply to 45 are 9 and 6, 9 and 5 right 9 and 5. Okay so I’m going to have square root of 9, times square root of 5 times square root of x there. Square root of 9 I know is regular 3 multiplied by -3, that’ll give me 9 square roots of 5x. Now this problem is ready to be simplified because I have 3 different terms that they all have the same radicals. 5 plus 8 is 13 13 minus 9 is 4, so my final answer will be 4 square roots of 5x.

Who would have thought that this whole nasty thing would come out with that little small answer? That’s why I kind of like these problems. You’re just looking for the factors that multiply to whatever is near radicand and once you have them simplified, it’s almost just like combining like terms.