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.
- Iggy RockoLv 75 months ago
(π − √3)(π + √3) =
pi^2 - 3
pi^2 is irrational so pi^2 - 3 is too.
- lenpol7Lv 75 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!!!!
- ?Lv 75 months ago
(π − √3)(π + √3) = π² - 3 is IRRATIONAL............ANS
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- rotchmLv 75 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].
- LônLv 75 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.
- mizooLv 75 months ago
(π − √3)(π + √3) = π^2 − √3^2
= π^2 − 3 => is an irrational number.
- DavidLv 75 months ago
It multiplies out as pi^2 -3 which works out as an irrational number
- Ian HLv 75 months ago
It comes to π^2 - 3 which is an irrational number because of π^2