anonymous
  • anonymous
simplifying radicals √3 ÷ √6
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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OakTree
  • OakTree
So we can write the following:\[\frac{ \sqrt 3 }{ \sqrt 6 } = \sqrt \frac{ 3 }{ 6 }\]And then simplify the inside. What do you get?
anonymous
  • anonymous
um .5
OakTree
  • OakTree
Right, but for now we'll keep it as 1/2. So then that's\[\sqrt \frac{ 1 }{ 2 } = \frac{ \sqrt 1 }{ \sqrt 2 } = \frac{ 1 }{ \sqrt 2 } = \frac{ \sqrt 2 }{ 2 }\]Do you get it?

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anonymous
  • anonymous
not really
OakTree
  • OakTree
What part don't you understand?
anonymous
  • anonymous
why did you take off the √ of 1 then it went to √2/ 2
OakTree
  • OakTree
Let's take it piece by piece. For the first part, what's the square root of 1?
anonymous
  • anonymous
1
OakTree
  • OakTree
Right. So we can essentially just take off the square root. Good?
anonymous
  • anonymous
yes
OakTree
  • OakTree
Great. So now for the second part - that's called rationalizing. Mathematicians don't like square roots in the denominator of fractions, so we do the following:\[\frac{ 1 }{ \sqrt 2 } = \frac{ 1 }{ \sqrt 2} \times \frac{ \sqrt 2 }{ \sqrt 2 } = \frac{ \sqrt 2 }{ \sqrt 2 \times \sqrt 2 } = \frac{ \sqrt 2 }{ 2 }\]Does that make sense now?
anonymous
  • anonymous
|dw:1378082372638:dw|
OakTree
  • OakTree
Exactly. So you get it?
anonymous
  • anonymous
yes
OakTree
  • OakTree
Great. Glad to help.
anonymous
  • anonymous
so this is a different equation 2÷√2 = 2÷2
anonymous
  • anonymous
is that correct
OakTree
  • OakTree
No, not quite. You can't just magically turn the square root of 2 into just 2. Why do you think that would work?
anonymous
  • anonymous
idk cause nothing can go to 2
OakTree
  • OakTree
What do you mean by that?
anonymous
  • anonymous
i dont know
anonymous
  • anonymous
im confused
OakTree
  • OakTree
Okay. Let me clarify. You can't take off a square root unless the number is 1. For all the other numbers, if you multiply a square root by itself, you get the number. Like if you look at the square root of 9, it's 3, right? And 3 times 3 is 9 again. Get it?
anonymous
  • anonymous
i think
anonymous
  • anonymous
i do
OakTree
  • OakTree
Great. So do you need help on anything else, or are you good?
anonymous
  • anonymous
so how would i solve this equation 2/√2
OakTree
  • OakTree
Well, you would multiply the top and bottom by sqrt(2) and you would get sqrt(2) on its own.
anonymous
  • anonymous
so it would be 1
anonymous
  • anonymous
2/2 is 1
OakTree
  • OakTree
No. Like this:\[\frac{ 2 }{ \sqrt 2 } \times \frac{ \sqrt 2 }{ \sqrt 2 } = \frac{ 2\sqrt 2 }{ 2 } = \sqrt 2\]Get it?
anonymous
  • anonymous
|dw:1378083150911:dw|
OakTree
  • OakTree
That's right, what you have there.
anonymous
  • anonymous
yeah but what happen to 2√2/2
OakTree
  • OakTree
The 2's cancel.
anonymous
  • anonymous
okay thanks
OakTree
  • OakTree
No problem.
anonymous
  • anonymous
so how about this equation √16 ÷ √12 = 2√2 ÷ 2√3

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