Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

InsanelyChaotic

Can you help me simplify a radical below?

  • one year ago
  • one year ago

  • This Question is Closed
  1. InsanelyChaotic
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\sqrt 80 - 3 \sqrt 63 - \sqrt 125 - \sqrt 175\]

    • one year ago
  2. KingGeorge
    Best Response
    You've already chosen the best response.
    Medals 0

    Let's go through these one at a time. First, let's simplify \(\sqrt{80}\). If we factor 80, we get \(80=2\cdot2\cdot2\cdot2\cdot5\). Since there are four 2's, we can say that \[\sqrt{80}=\sqrt{2^4\cdot5}=2^2\sqrt{5}=4\sqrt{5}\]Did this all make sense?

    • one year ago
  3. 03453660
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1351701634673:dw|

    • one year ago
  4. InsanelyChaotic
    Best Response
    You've already chosen the best response.
    Medals 0

    @KingGeorge Where did the 2's come from?

    • one year ago
  5. InsanelyChaotic
    Best Response
    You've already chosen the best response.
    Medals 0

    When I see myself factoring, the number two doesn't even come to mind, do you just pick any number?

    • one year ago
  6. 03453660
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1351701840947:dw|

    • one year ago
  7. 03453660
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1351701946360:dw|

    • one year ago
  8. KingGeorge
    Best Response
    You've already chosen the best response.
    Medals 0

    There are certain numbers that you should think about when you're factoring this kind of number. In particular, they're the "prime" numbers. The first few prime numbers are 2,3,5,7,11,13. When you're trying to simplify radicals, see if you can divide the number by these "prime" numbers. Usually, we start at the smallest one. So for 80, you can divide by 2 to get \(80=2\cdot 40\). Again, we notice that 2 divides 40, so we get \(80=2\cdot2\cdot20\). Keep doing this, and we get \[80=2\cdot2\cdot2\cdot10\]\[80=2\cdot2\cdot2\cdot2\cdot5\]Since 5 is on our list of prime numbers, we stop, because we can't divide any more.

    • one year ago
  9. InsanelyChaotic
    Best Response
    You've already chosen the best response.
    Medals 0

    That's incredible, thank you for taking the time to explain that

    • one year ago
  10. KingGeorge
    Best Response
    You've already chosen the best response.
    Medals 0

    So if you follow this same process, you should get almost what 03453660 did (175 is a bit different). In particular,\[80=2^4\cdot 5\]\[63=3^3\cdot7\]\[125=5^3\]\[175=5^2\cdot 7\]Now, can you take the square roots of the factored numbers?

    • one year ago
  11. InsanelyChaotic
    Best Response
    You've already chosen the best response.
    Medals 0

    Can I what?

    • one year ago
  12. InsanelyChaotic
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm sorry, that question caught me off guard

    • one year ago
  13. KingGeorge
    Best Response
    You've already chosen the best response.
    Medals 0

    So we already said that \(\sqrt{2^4\cdot5}=4\sqrt{5}\). Now, what is \[\large \sqrt{3^2\cdot 7}?\]Also, I've got go now, feel free to call in someone else to help you finish.

    • one year ago
  14. InsanelyChaotic
    Best Response
    You've already chosen the best response.
    Medals 0

    12x7?

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.