Question

Simplify square root of negative 48.

Answer 1

Can you think of any perfect squares that are factors of 48?

Answer 2

no not from the top of my head

Answer 3

its \[\sqrt{-48}\]

Answer 4

I understand, but there's a method to my madness. You're going to have to simplify this radical, so you'll need to do this.
The first few prefect squares are 1, 4, 9, 16, 25, 36, 49, etc. What is the largest of these that is a factor of 48?

Answer 5

4? because 4x12 is 48

Answer 6

That's right, but is there a larger one?

Answer 7

I'm really rusty on my times table facts

Answer 8

Use a calculator if it helps

Answer 9

ok

Answer 10

24

Answer 11

Sorry, 24 is not a perfect square. I listed them above. What's the largest one that is a factor of 48?

Answer 12

I'm confused a bit, wouldn't it be 4? because 9x9 is 81 and thats too big

Answer 13

9 is a perfect square because 3 x 3 = 9
16 is a perfect square because 4 x 4 = 16
25 is a perfect square because 5 x 5 = 25
etc.
Which of those listed numbers is the largest one that is a factor of 48? You don't need to square them.

Answer 14

36

Answer 15

Excellent. 16 x 3 = 48.

Answer 16

now what?

Answer 17

Now, we're going to use the rules of working with radicals to simplify. Your question is\[\sqrt{-48}\]Having identified the largest perfect square that is a factor of 48 we can rewrite as follows\[\sqrt{-48}=\sqrt{\left( 16 \right)\left( -1 \right)\left( 3 \right)}\]Understand what we did here?

Answer 18

yes

Answer 19

Good. Now the rules of radicals say that we can write this as follows\[\sqrt{-48} = \sqrt{\left( 16 \right)\left( -1 \right)\left( 3 \right)} = \sqrt{16}\sqrt{-1}\sqrt{3}\]You OK with that?

Answer 20

ok

Answer 21

Good. You know what the square root of 16 is? And the square root of -1?

Answer 22

yes its 4 but i don't know the square root of -1

Answer 23

You haven't studied imaginary numbers?

Answer 24

no, I'm learning them right now thats why i need help

Answer 25

Well imaginary numbers are based on the square root of -1. It is an imaginary number that is given the symbol i. In other words\[\sqrt{-1} = i\]

Answer 26

So, you have \(\sqrt{16} \sqrt{-1} \sqrt{3}\). And you know the square root of 16 and the square root of -1. Just substitute them in.

Answer 27

these are my answer choices
negative 4 square root of 3
4 square root of negative 3
4 i square root of 3
4 square root of 3 i

Answer 28

\[\sqrt{16}\sqrt{-1}\sqrt{3} = ?\]

Answer 29

would it be b or d?

Answer 30

\(\sqrt{16}=4\) and \(\sqrt{-1} = i\) and \(\sqrt{3}\) can't be simplified any further. What does that give you?

Answer 31

D!?

Answer 32

Well, the individual parts of D are correct but they're in the wrong order. Should have the rational number first, then the imaginary number i, then the radical. What other choice meets this description?

Answer 33

C then?

Answer 34

That's correct. It's the convention that we write the answer \(4i\sqrt{3}\) rather than \(4\sqrt{3}i\) or \(\sqrt{3}i4\) or any other combination.

Answer 35

ok, thank you i was confused but now i understand better

Answer 36

You're welcome