anonymous
  • anonymous
I understand absolutely nothing about square roots...help! What is the exact value of the expressions the square root of 180. − the square root 125. + the square root of 5.? Simplify if possible. 2the square root of 2. 12the square root of 2. 2the square root of 5. 12the square root of 5.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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mathmale
  • mathmale
the square root operator is the inverse of the power operator. Given y=x^2, the inverse is x=Sqrt(y). Given y=25, the inverse is Sqrt(25), or 5.
mathmale
  • mathmale
What is the square root of 180? We need to factor 180. To do this, we look for the LARGEST PERFECT SQUARE that divides into 180 with no remainder. To do this, list perfect squares: 1, 4, 16, 25, 36, 49, 81, and so on. Which of these divides into 180 with no remainder? Show 180 in factored form.
anonymous
  • anonymous
i dont know what that means...

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mathmale
  • mathmale
Divide 4 into 180. Divide 9 into 180. Divide 16 into 180. And so on. Which of these perfect squares divides into 180 with no remainder?
anonymous
  • anonymous
9?
mathmale
  • mathmale
\[\frac{ 180 }{ 9 }=\frac{ 90*2 }{ 9 }=\frac{ 9*10*2 }{ 9 }\]
mathmale
  • mathmale
=20, with no remainder. Yes.
mathmale
  • mathmale
So, your 180 factors into 9*20. Unfortunately, we 're not done yet, since 20 factors into 4*5, and 4 is a perfect square. Can you now reduce 180=9*20=9*(FACTORS OF 20)?
anonymous
  • anonymous
what does that mean?
mathmale
  • mathmale
Let's put it a different way. Determine the factors of 20.
mathmale
  • mathmale
Which two numbers, multiplied together, result in your obtaining 20?
anonymous
  • anonymous
2 and 10, 4 and 5 and 1 and 20
mathmale
  • mathmale
Very good. Now, which of these is a perfect square? {2, 10, 4, 5}
anonymous
  • anonymous
4?
mathmale
  • mathmale
Yes. So, your 9*10*20 becomes 9*10*4*5. Note that 9*4=36, a perfect square. So, 180=36* ( ? )
mathmale
  • mathmale
This discussion is needlessly complicated. Sorry. But it does help to practice factoring, identifying perfect squares, and so on.
anonymous
  • anonymous
5
mathmale
  • mathmale
Right. So, what are all the factors of 180? First list those that are perfect squares, and then list those that are not perfect squares.
anonymous
  • anonymous
i dont know which re perfect squares
anonymous
  • anonymous
i think the answer is c but idk how to justify that
mathmale
  • mathmale
{1, 2, 3, .... ? } Perfect squares include {1, 4, 9, 16, 25, 36, 49, 64, 81, 100, and so on.} Earlier I typed the following to you: Yes. So, your 9*10*20 becomes 9*10*4*5. Note that 9*4=36, a perfect square. So, 180=36* ( ? ) You responded (later) with 5. Thus, 180=36*5. Note that 36 is a perfect square (it comes from 9*9 or 9^2), and that 36 is also the LARGEST perfect square that will divide into 180.
mathmale
  • mathmale
You are supposed to find the exact square root of 180 in this problem.
mathmale
  • mathmale
Since 180 = 36 * 5, \[\sqrt{180}=\sqrt{36}*\sqrt{5}\]
mathmale
  • mathmale
Find the sqrt of 36. \[\sqrt{36}=?\]
anonymous
  • anonymous
is 6?
mathmale
  • mathmale
Yes. So,\[\sqrt{180}=\sqrt{36}*\sqrt{5}=6\sqrt{5}\]
mathmale
  • mathmale
Next one is 125. What is the exact square toot of 125? I ask you to do the same thing as before. Find the largest perfect square factor of 125. Hint: It's one of these; {9, 16, 25, 49}.
anonymous
  • anonymous
25?
mathmale
  • mathmale
Harley? I need your attention.
anonymous
  • anonymous
yes
anonymous
  • anonymous
?
mathmale
  • mathmale
What is the square root (exact square root) of 125? Again I ask you to find the largest perfect square factor of 125. I gave you a list from which to choose. See above.
anonymous
  • anonymous
so its not 25?
mathmale
  • mathmale
It is indeed 25. What's the other factor of 125?
anonymous
  • anonymous
5
mathmale
  • mathmale
Cool. Then,\[\sqrt{125}=\sqrt{25}\sqrt{5}\]
mathmale
  • mathmale
Re-write this in simplest form. That means finding the square root of 25. \[\sqrt{125}=( ? )\sqrt{\sqrt{5}}\]
anonymous
  • anonymous
also 5?
mathmale
  • mathmale
\[\sqrt{125}=5\sqrt{5}\]
mathmale
  • mathmale
is all you need.
anonymous
  • anonymous
what answer choice would it be though?
mathmale
  • mathmale
I've just reviewed your original posting. You are to write a mathematical expression for "180. − the square root 125. + the square root of 5. You already know that Sqrt(180)=6Sqrt(5), and you know the Sqrt of 125. Write out the 3 terms in that order. I'm sorry, but I need to get off the 'Net. I'd be happy to continue working with you later today. Thanks for your hard work and patience.
anonymous
  • anonymous
okay thank you so much

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