In Exercises 11–28, add or subtract as indicated. You will need t...

Question

In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals.
___ ___
5√45x - 2√20x

Accepted Answer

Hey, everyone in this problem, we're asked to perform subtraction of radicals. After simplification, the expression we're given is 12, multiplied by the square root of 125 x -9, multiplied by the square root of 80 x. We're given four answer choices. Option A is 24 multiplied by the square root of two X. Option B is 96 multiplied by the square root of 2 x. Option C is 24 multiplied by the square root of 5 x and option D is multiplied by the square root of five. We're gonna start by rewriting what we were given. So we have 12 multiplied by the square root of 125 x minus nine multiplied by the square root of 80 x. Now, we want to simplify these radicals. OK. These square roots as much as we can, we're not going to be able to simplify the square root of X. That's as simple as it can get, but maybe we can simplify these constants. OK? So let's try to write them as something that we can take the square root of and get an integer multiplied by something else. So we have 12 multiplied by the square root. Now 125, the square root is not going to be a nice integer, but we can write a 125 as multiplied by fat. So we have 25 multiplied by 5 x and then we have -9 multiplied by the square root. And we're gonna do the same thing with 80. Maybe we wanna write 80 as something that we can take the square root of and get an integer multiplied by something else that turns out to be 16, multiplied by five. So we have 16, multiplied by five xx under this square. OK. So now I'm broken up our terms underneath the square root. But how can we actually evaluate them or recall if we have the nth root of X multiplied by Y, we can write this as the N root of X multiplied by the end through of Y. OK. So if we have two things multiplied together underneath our root, we can split them up, take the root of each of those terms separately and then multiply the result together. So in our case, we can write this as 12 multiplied by the square root of 25, multiplied by the square root of 5 x -9, multiplied by the square root of 16 multiplied by the square root of 5 x. So we have 12, the square of 25 is five So we have multiplied by five, multiplied by the square root of 5x. Yeah, we can't simplify that any further. And then we have minus nine, the square root of 16 is four. So we get nine multiplied by four, multiplied by the square root of five X. Simplifying each of these 12 multiplied by five gives us 60. So we have 60 multiplied by the square root of 5 x nine multiplied by four gives us 36. So then we have minus 36 multiplied by the square root of five X. So 60 multiplied by the square root of five X minus 36 multiplied by the square root of five X gives us 24 multiplied by the square root of 5x. And that is the result we were looking for. That's as simple as we can make this, we can't simplify any of these terms further. And so the result is 24 multiplied by the square root of 5 x which corresponds with answer choice. C thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. _ _ 5√45x - 2√20x

Key Concepts

Radical Expressions

Like Radicals

Simplifying Radicals

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