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iwanttogotostanford
 one year ago
Simplify square root of negative 48.
iwanttogotostanford
 one year ago
Simplify square root of negative 48.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can you think of any perfect squares that are factors of 48?

iwanttogotostanford
 one year ago
Best ResponseYou've already chosen the best response.0no not from the top of my head

iwanttogotostanford
 one year ago
Best ResponseYou've already chosen the best response.0its \[\sqrt{48}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.04? because 4x12 is 48

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's right, but is there a larger one?

iwanttogotostanford
 one year ago
Best ResponseYou've already chosen the best response.0I'm really rusty on my times table facts

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Use a calculator if it helps

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, 24 is not a perfect square. I listed them above. What's the largest one that is a factor of 48?

iwanttogotostanford
 one year ago
Best ResponseYou've already chosen the best response.0I'm confused a bit, wouldn't it be 4? because 9x9 is 81 and thats too big

anonymous
 one year ago
Best ResponseYou've already chosen the best response.09 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Excellent. 16 x 3 = 48.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now, 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Good. 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Good. You know what the square root of 16 is? And the square root of 1?

iwanttogotostanford
 one year ago
Best ResponseYou've already chosen the best response.0yes its 4 but i don't know the square root of 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You haven't studied imaginary numbers?

iwanttogotostanford
 one year ago
Best ResponseYou've already chosen the best response.0no, I'm learning them right now thats why i need help

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well 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
 one year ago
Best ResponseYou've already chosen the best response.0So, 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
 one year ago
Best ResponseYou've already chosen the best response.0these 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
 one year ago
Best ResponseYou've already chosen the best response.0\[\sqrt{16}\sqrt{1}\sqrt{3} = ?\]

iwanttogotostanford
 one year ago
Best ResponseYou've already chosen the best response.0would it be b or d?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\sqrt{16}=4\) and \(\sqrt{1} = i\) and \(\sqrt{3}\) can't be simplified any further. What does that give you?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That'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
 one year ago
Best ResponseYou've already chosen the best response.0ok, thank you i was confused but now i understand better
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