Help with surds maths question?

π is an irrational number and so is √3. Therefore, determine whether

(π − √3)(π + √3) is an irrational number.

9 Answers

Relevance
  • 5 months ago

    (π − √3)(π + √3) =

    pi^2 - 3

    pi^2 is irrational so pi^2 - 3 is too.

  • 5 months ago

    (pi - sqrt(3)(pi _ sqrt(3)

    Multiply together using FOIL

    pi^2 - pisqrt(30 + pisqrt(3) - 3

    Hence collecting terms

    pi^2 - 3

    9.869604401.... - 3

    = 6.869604401.... which is irrational!!!!

  • 5 months ago

    pi^2 is irrational

    see https://planetmath.org/piandpi2areirrational

    therefore (π − √3)(π + √3) = π^2 - 3 is irrational

  • ?
    Lv 7
    5 months ago

    (π − √3)(π + √3) = π² - 3 is IRRATIONAL............ANS

  • What do you think of the answers? You can sign in to give your opinion on the answer.
  • rotchm
    Lv 7
    5 months ago

    Developing as others have here for you, you get the answer π² - 3.

    You must now verify if this is irrational or not.

    If it were rational then π² - 3 = a/b for some integers a & b. Thus

    π² = a/b + 3 = rational = A/B for integers A & B.

    Thus you question becomes one in finding if π² is rational or not.

    For this, depends on what tools you have (what grade you are in). Just from your info, we cant

    say if π² is rational or not. [But yes, π² is irrational. This can be shown by various means. Perhaps the simplest relies on knowing that π is transcendental].

  • Lôn
    Lv 7
    5 months ago

    (π − √3)(π + √3)

    π(π − √3) + √3 (π - √3)

    π^2 - √3π + √3π - 3

    π^2 - 3

    So it is an irrational number as you can't express it as a fraction.

  • mizoo
    Lv 7
    5 months ago

    (π − √3)(π + √3) = π^2 − √3^2

    = π^2 − 3 => is an irrational number.

  • David
    Lv 7
    5 months ago

    It multiplies out as pi^2 -3 which works out as an irrational number

  • Ian H
    Lv 7
    5 months ago

    It comes to π^2 - 3 which is an irrational number because of π^2

Still have questions? Get answers by asking now.