Square root questions

  1. I feel embarassed to ask these questions but what is the rule for to simplify division, addition, and subtraction square roots? Here are some questions:

    SIMPLIFY:


    [tex]5\sqrt{24}\div2\sqrt{18}[/tex]



    [tex]\sqrt{40} + \sqrt{90}[/tex]




    [tex]\sqrt{50} - \sqrt{18}[/tex]
     
  2. jcsd
  3. cristo

    cristo 8,407
    Staff Emeritus
    Science Advisor

    What have you tried? You need to simplify the square roots. For example, write the first question as [tex]\frac{5\sqrt{24}}{2\sqrt{18}}[/tex] Now, can you simplify [itex]\sqrt{24}[/itex] and [itex]\sqrt{18}[/itex]?

    [Hint: write each number under the sqrt sign as a product of primes.]
     
  4. Sorry, I meant to write the question like a fraction I just didn't know the code. When you are simplifying roots, and you take out lets say the root of 4, do you times the number already outside the root sign by 2?


    [tex]\frac{5\sqrt{24}}{2\sqrt{18}}[/tex]
    =[tex]\frac{5\sqrt{4*6}}{2\sqrt{3*6}}[/tex] (don't know what to do, so long since we had done radicals)
     
    Last edited: Apr 4, 2007
  5. hage567

    hage567 1,539
    Homework Helper

    "When you are simplifying roots, and you take out lets say the root of 4, do you times the number already outside the root sign by 2?"

    Yes.
     
  6. Also, remember to rationalize the fraction^^
     
  7. cristo

    cristo 8,407
    Staff Emeritus
    Science Advisor

    [tex]\frac{5\sqrt{4*6}}{2\sqrt{3*6}}=\frac{5\cdot 2\cdot\sqrt{6}}{2\cdot\sqrt{3}\cdot\sqrt{6}}[/tex]

    Can you simplify this?
     

  8. [tex]\sqrt{40} + \sqrt{90}[/tex]=[tex]\sqrt{4*10}+\sqrt{9*10}[/tex]=2[tex]\sqrt{10}+3\sqrt{10}[/tex]=

    can you go from here??
     
  9. this may confuse you more but when you add fractions you need to get the denominator (number on the bottom of fraction) the same. The same goes with surds (square roots), you need to get the number inside the root the same on each surd in oder to add/subtract.


    I find it harder to do the + - surds than the x and / surds

    When you divide:
    [tex] \sqrt{a} \div \sqrt{b} = \frac {\sqrt{a}}{\sqrt{b}}[/tex] which is also written as [tex]\sqrt{\frac{a}{b}}[/tex]

    Have a look

    http://www.mathsrevision.net/gcse/pages.php?page=6

    and

    http://www.bbc.co.uk/schools/gcsebitesize/maths/numberih/surdshrev2.shtml
     
    Last edited: Apr 5, 2007
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