in-19-34-write-each-sum-or-difference-in-terms-of-i-sqrt-25-sqrt-4

Question

In $19-34,$ write each sum or difference in terms of $i$
$$
\sqrt{-25}-\sqrt{-4}
$$

Martha Richards · Accepted Answer

Okay, So our next problem here is the square root of negative 25 minus the square root of a negative four. And they want us to put this in terms of by. And so this negative 25 is a perfect square. So I have a negative one tens and 20 square root of 25 minus again, this negative one in a square root of four. Cause this four is also a perfect square. So this guy here is I and this is five. So I have five. I minus. This is I And this is 22 I. And because these air like terms, we can combine these and this is equal to three I.

Martha Richards · Answer

our next problem here is another couple of perfect square. So I have a negative 49 minus the square root of negative 16. So I take out my negative one. I keep that 49 minus the square to negative one. Tend to square 2 16 So this is I and this is seven. So I have seven. I minus This is I and this is for so I have minus of four I and so this we can combine because of, like, terms. And I get a three I

Martha Richards · Answer

Okay, so we have this time a two times and negative square root of a negative five plus the square root of a negative 1 25 So here we keep that too, And the square root. And they want us to put this in terms of I. So we have that negative one time the square root of five. And then plus, we&#x27;ve got to find our perfect square in here. And that&#x27;s a 25. No. Yeah, that&#x27;s a 25 times five. So then I have that negative one times the square root of 25 times the square root of five. And so here we know that this is I in the square root of five stays as this. Why have a two i square root five and then a plus, this guy here turns into an eye. This is a five in the square root of five stays as is So I have been a five I square route five. And because I have the same i this imaginary number, I have I and the square root of five. Because I have the exact same radical and this imaginary number here I can combine these real numbers and so this becomes a seven I square root of five

Martha Richards · Answer

Okay, so this one got just a bit more complicated. So I have a square root of 50 plus a square root of a negative too. Plus the square root of 200 plus the square root of negative 50. And so they want us to combine our like terms and get it into terms of I. So here, this 50 this 50 it&#x27;s perfect. Square is a 25 in it too. And so same goes for this guy here. And then this one here is a two time The 100 is This is our biggest perfect square. And our negative too, is the smallest it can be. And so here, this has no negative in front of it. So I just take the swear to 25 times a squared it two plus and this one does. So I&#x27;m gonna take out that negative and then here, plus the square root of 100 the square root of two, and then hear that negative one I have. So that&#x27;s that. And then the square root of 25 times the square root of two. So we&#x27;ll take this guy one step at this time, so I have this turns into a five. So I have five square root, too. And then this here plus sign, I haven&#x27;t I and a square root of two. And then here I have a 10 and a square root of two. So plus 10 square root, too. And then here&#x27;s an eye. This is five square to 25 5 in the square root of two stays as it is so, plus, ah five I square root of two. So here we cannot combine this five square to two in the ice core to two because they both need to have that imaginary number so you can see that I can combine those two terms. And then I can combine these two terms. So a five plus a 10 is 15 square root of two, and then a five I plus an eye is plus six I square root of two

Martha Richards · Answer

Okay. Next problem Here. I have a negative two, plus a square root of negative 16 plus seven minus a negative. 49. And so I can again combine these numbers. So I have a five and negative two plus seven is five. And then plus this is a perfect square. And this is a perfect square, so I don&#x27;t need to do anything. I don&#x27;t have to factor the east. I could just do a negative one times a square root squared, negative one times the square root of negative of square root of 16. And then here I have a minus. And this is a square root of negative one times the square root of 49. So this five stays as is This becomes I. This is for so I have plus a fee four eye in this minus sign. And then this is an I. And this is a seven. So I have minus seven. I I can combine these. So I get a five minus a three. I

Martha Richards · Answer

Okay, so our next problem here does look a little scary, I&#x27;ll admit. But don&#x27;t worry, this is not as bad as it seems. So what we&#x27;ve got here is the square root of 0.2025 and that&#x27;s plus a square root of negative 0.9. So when you look at these numbers this nine and this number here, you should think that they probably do have, uh you can take the perfect square root here, and you&#x27;d indeed can. So you pull out your calculator here, and you would find that the square root of this number here is a 0.45 and then plus, and I have my square with a one year, and you&#x27;re going to use your calculator to find the perfect square of this 10.9. So this here is an eye, and this is a 0.3. So what I&#x27;m left with here is this. 0.45 plus a zero point three I

Problem

In $19-34,$ write each sum or difference in terms…

Problem 20 Easy Difficulty

In $19-34,$ write each sum or difference in terms of $i$
$$
\sqrt{-25}-\sqrt{-4}
$$

Answer

3$i$

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Ann Xavier Gantert

Algebra 2 and Trigonometry