iwanttogotostanford
  • iwanttogotostanford
Simplify square root of negative 48.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Can you think of any perfect squares that are factors of 48?
iwanttogotostanford
  • iwanttogotostanford
no not from the top of my head
iwanttogotostanford
  • iwanttogotostanford
its \[\sqrt{-48}\]

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anonymous
  • anonymous
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?
iwanttogotostanford
  • iwanttogotostanford
4? because 4x12 is 48
anonymous
  • anonymous
That's right, but is there a larger one?
iwanttogotostanford
  • iwanttogotostanford
I'm really rusty on my times table facts
anonymous
  • anonymous
Use a calculator if it helps
iwanttogotostanford
  • iwanttogotostanford
ok
iwanttogotostanford
  • iwanttogotostanford
24
anonymous
  • anonymous
Sorry, 24 is not a perfect square. I listed them above. What's the largest one that is a factor of 48?
iwanttogotostanford
  • iwanttogotostanford
I'm confused a bit, wouldn't it be 4? because 9x9 is 81 and thats too big
anonymous
  • anonymous
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.
iwanttogotostanford
  • iwanttogotostanford
36
anonymous
  • anonymous
Excellent. 16 x 3 = 48.
iwanttogotostanford
  • iwanttogotostanford
now what?
anonymous
  • anonymous
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?
iwanttogotostanford
  • iwanttogotostanford
yes
anonymous
  • anonymous
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?
iwanttogotostanford
  • iwanttogotostanford
ok
anonymous
  • anonymous
Good. You know what the square root of 16 is? And the square root of -1?
iwanttogotostanford
  • iwanttogotostanford
yes its 4 but i don't know the square root of -1
anonymous
  • anonymous
You haven't studied imaginary numbers?
iwanttogotostanford
  • iwanttogotostanford
no, I'm learning them right now thats why i need help
anonymous
  • anonymous
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\[\sqrt{-1} = i\]
anonymous
  • anonymous
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.
iwanttogotostanford
  • iwanttogotostanford
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
anonymous
  • anonymous
\[\sqrt{16}\sqrt{-1}\sqrt{3} = ?\]
iwanttogotostanford
  • iwanttogotostanford
would it be b or d?
anonymous
  • anonymous
\(\sqrt{16}=4\) and \(\sqrt{-1} = i\) and \(\sqrt{3}\) can't be simplified any further. What does that give you?
iwanttogotostanford
  • iwanttogotostanford
D!?
anonymous
  • anonymous
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?
iwanttogotostanford
  • iwanttogotostanford
C then?
anonymous
  • anonymous
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.
iwanttogotostanford
  • iwanttogotostanford
ok, thank you i was confused but now i understand better
anonymous
  • anonymous
You're welcome

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