Results 1 to 3 of 3

Math Help - is this proof correct?

  1. #1
    Newbie
    Joined
    May 2012
    From
    San Diego
    Posts
    5

    is this proof correct?

    Theorem: for all non-negative real numbers a and b, SQRT(a*b) = SQRT(a)*SQRT(b)

    Proof: suppose a and b are any non negative real numbers. Then there exists unique non negative real numbers m and n such that a = m2 and b = n2. Then

    a*b = m2*n2 by substitution
    = (m*n)2 by laws of exponents.

    Then by taking the square root of both sides

    SQRT(a*b) = m*n

    but because a = m2 and b = n2, it follows that m = SQRT(a) and n = SQRT(b), and so , by substitution

    SQRT(a*b) = SQRT(a)*SQRT(b)
    Q.E.D

    Thanks in advanced for your comments
    Last edited by ga04; May 18th 2012 at 11:12 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member Sarasij's Avatar
    Joined
    Jun 2011
    From
    India
    Posts
    42
    Thanks
    2

    Re: is this proof correct?

    Quote Originally Posted by ga04 View Post
    Theorem: for all non-negative real numbers a and b, SQRT(a*b) = SQRT(a)*SQRT(b)

    Proof: suppose a and b are any non negative real numbers. Then there exists unique non negative real numbers m and n such that a = m2 and b = n2. Then

    a*b = m2*n2 by substitution
    = (m*n)2 by laws of exponents.

    Then by taking the square root of both sides

    SQRT(a*b) = m*n

    but because a = m2 and b = n2, it follows that m = SQRT(a) and n = SQRT(b), and so , by substitution

    SQRT(a*b) = SQRT(a)*SQRT(b)
    Q.E.D

    Thanks in advanced for your comments
    I think this is an absolutely correct proof because the problem is just to show the result holding for "Non-Negative" reals only...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2012
    From
    Irving TX
    Posts
    42
    Thanks
    1

    Re: is this proof correct?

    Yes of-course this proof is correct, as this proof is satisfying the given theorem.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Correct proof?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 12th 2011, 01:14 PM
  2. Is this proof correct?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 11th 2010, 12:13 PM
  3. lcm, gcd proof correct?
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 26th 2010, 06:32 AM
  4. Proof of n^5 = n mod 5 .. is this correct?
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 9th 2006, 08:24 PM
  5. Is proof correct?
    Posted in the Algebra Forum
    Replies: 13
    Last Post: January 13th 2006, 10:35 AM

Search Tags


/mathhelpforum @mathhelpforum