Adding and simplifying radicals | Exponent expressions and equations | Algebra I | Khan Academy

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We are now required to add and simplify the square root of 2x ^ 2 + 4 x Square Root of 8 + 3 x Square Root of 2x ^ 2 + Square Root of 8 So we’re going to do a little bit of addition, so we can simplify First, then we collect, or we can first, and then we simplify But it looks like we can do the addition, so let’s try to do that Here, we have the square root of 2x ^ 2, and here I have three square roots For 2x ^ 2, well, if I have one element of one thing here and I have three elements of something else here, and I want If I add them together, I can put a parameter here, and to make this clear, I have one element here Here I have three elements, and all I want is to group them together, therefore I will get four elements, that is, I have a 4 x square root of 2x ^ 2 This is a bit annoying, imagine that the square root of 2x is variables We will say that all of this is “a” and this is also “a”, because they are the same thing, we will have one “a” + 3 “a”, so the result is 4 “a”, in this case “a” is all of this here And what we did was we brought them together, and then we have to think about what it means to have 4 square roots of “a” and we also have An extra square root of “a”, with the same idea that we have 4 of these elements – I\’m going to set them in purple – I have another element of this that I have specified in purple, which is the parameter So I have 4 elements + one more item so the total is five So + 5 x the square root of 8 And now we’ll see if we can simplify it, we have 4 elements, plus 5 more We cannot combine these two elements only, and hopefully we can simplify the statement a little We know that the square root of 2x ^ 2 is equal – let me write the 4 Outside of the expression – so we have 4, and the square root of 2x ^ 2 is equal to the square root For 2 x square root of x ^ 2, I’m going to rewrite this part here Then we have, + 5 x, the 8 can be written in complete square and Incomplete square, so 8 can be written 4 x 8, so let’s write it this way It becomes the square root of 4×2, and we can rewrite the phrase as follows: 5 x The square root of 4 x The square root of 2 What can we simplify here? Well, we know that the x ^ 2 root is the positive square root For x ^ 2, so this is not just x, and if you want to think of it as this, it really is Positive square root, and we have to say it is the absolute value of x, because what if x is negative? If it were, suppose we had -3, so we would have -3 ^ 2 And we get the result positive 9, so the square root of positive 9 will be positive 3 So what we have is not just x, but also not a negative value ie -3, but 3, so we have To take the absolute value, and the other number that is considered a whole square is 4, so take root Squared is 2, and now we have, if we change the order, then We will multiply our 4, 4 x | x | 4 x | x | X The square root of 2 I want to write this in the same yellow, x square root of 2 + 5 x 2, i.e. 10, and all of this can be simplified to 2, so we have + 10 The square root of 2, now it can be said that we have accomplished all addition and simplification operations Or more plural operations can be done based on how you want to consider them, because we have it here 4 x | x | The square root of 2, and here we have 10 the square root of 2 So we have four elements of | x |, and 10 elements of the same thing, so you can Combine them together, or you can think another way, you could take the square root of 2 as a common factor You get 4 x | x | + 10 x square root of 2, depending on the simplified image that you have, which one Both are valid

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