in-3-18-write-each-number-in-terms-of-i-5-sqrt-27

Question

In $3-18,$ write each number in terms of $i$
$$
5 \sqrt{-27}
$$

Jennifer Spoerke · Accepted Answer

Let&#x27;s take a look at five times the negative have times the square root of negative 27. We&#x27;re going to first start by breaking up in this negative 27. The five is currently just coming along for the ride, so five times the square root of negative one times The square root of 27 27 is an irrational number, but we can break it up using a factor tree, and it turns into nine times three. Nine is a perfect square. Square root of nine square root of three square root of nine gives us three. The square root of three is also in irrational number, and what&#x27;s more is we know that the square root of negative one is I. So what this is going to give us is five times I times three times the square root of three. What we&#x27;re going to do is multiply this three with this five for an answer of 15 I Route three or, if you prefer 15. Route three. I

Jennifer Spoerke · Answer

Let&#x27;s take a look at the negative square root of negative 51. We&#x27;re gonna start by splitting negative 51 into negative one times 51. We&#x27;re looking at the square root. I was both. This negative sign is important. Keeps coming along with the red. So the square root of negative one is I. We have a negative 51. We need to see if there&#x27;s a perfect square hiding inside of 51. Let&#x27;s come over here and make a factor. Tree 51 is not divisible by two, but it is divisible by three. 51. Divided by three is 17. Both three and 17 are prime numbers, so we can&#x27;t really break up squared of 51 anymore than what it already is. So it&#x27;s going to stay has that 51 which means that our answer is negative. I radical 51 or, if you prefer negatives, radical 51. Hi,

Martha Richards · Answer

Okay, So this question is asking us to put Thescore air route of negative 81 into I format to imaginary number format. So what I&#x27;m gonna do is take out that negative one, and you can hopefully remember that an 81 is a perfect square. So nine times nine is 81. So this here is an eye and this is nine. So this is equal to nine. I

Jennifer Spoerke · Answer

The problem that we&#x27;re working on is the square root of negative nine. We&#x27;re gonna break this down into two different pieces the square root of negative one times nine which can be split again into the square root of negative one times the square root of nine. The square root of negative one is equal to the imaginary unit. I square root of nine is equal to three. Therefore, the square root of negative nine is equal. 23 I

Martha Richards · Answer

Okay, So again, we&#x27;re gonna put a number here, the square root of negative eight into terms of I. So this one here is not a perfect squares. What we&#x27;re going to do is we&#x27;ll take that that negative one first. And that&#x27;s times. And we have to figure out to reduce this guy. We&#x27;ve got to figure out, um, what perfect squares we can get out of eight. And we do know that a four times two gives us eight right? Four times too. And so this here is a perfect squares awaken, say, is the square root of four times the square root of two. And so here that our answer is this becomes an eye. This year becomes too, and this stays in. And so what we get in the notation for this is to put the number first, followed by the eye and then followed by the radical so that we if we put the eye afterwards, we&#x27;re not really sure if the rat if the eye goes inside the radical or not. So this is the common notation that we use for when we have a radical

Martha Richards · Answer

All right, So now we&#x27;re going to put a another number here that they&#x27;ve concocted into terms of I. So here they have a negative square root of negative 36. So we keep that negative sign, and then we have a square root of a negative one and 36 again is a perfect square. So we have the square root of 36. So then we have a negative, and this goes to ID. This is six. So we have a negative six, I

Problem

In $3-18,$ write each number in terms of $i$ $$ …

Problem 11 Medium Difficulty

In $3-18,$ write each number in terms of $i$
$$
5 \sqrt{-27}
$$

Answer

15$\sqrt{3} i$

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Algebra 2 and Trigonometry

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Absolute Value - Example 1

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15$\sqrt{3} i$

Algebra 2 and Trigonometry

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Absolute Value - Example 1

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Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Heather Z.

Maria G.

Kristen K.

Ann Xavier Gantert

Algebra 2 and Trigonometry