Yes, √3 + √5 is irrational.
It is irrational. Any number that cannot be written as a fraction is irrational. So if the Golden Ratio were rational, instead of a never-ending decimal number, you'd see a fraction. The official measurement is (1+sqrt5)/2. sqrt5 is irrational.
The golden ratio is not a rational number. It cannot be expressed exactly as the quotient of two integers. It can be expressed as the quotient: (1+SQRT5)/2 where SQRT5 menas the square root of 5 (that is not a rational number either and so no quitient involving it is a rational number)
Yes, if your equation is f(x) = sqrt5(x). The square root is also a function itself, if that's what you mean.
yes
Yes. The sum of two irrational numbers can be rational, or irrational.
It is irrational. Any number that cannot be written as a fraction is irrational. So if the Golden Ratio were rational, instead of a never-ending decimal number, you'd see a fraction. The official measurement is (1+sqrt5)/2. sqrt5 is irrational.
Two different irrationals can't make a rational...
Yes. It is equal to (1 + sqrt5) / 2 = ~1.618 which, though irrational, is a purely real number; i.e. it has no imaginary component.
Actually, I make it 3 - sqrt5 So before we attempt a proof, where did the sqrt5 - 1 result come from?
Evaluate (1+sqrt5)/2. This is equal to 1.6180
The golden ratio is not a rational number. It cannot be expressed exactly as the quotient of two integers. It can be expressed as the quotient: (1+SQRT5)/2 where SQRT5 menas the square root of 5 (that is not a rational number either and so no quitient involving it is a rational number)
Irrational. Irrational. Irrational. Irrational.
It is irrational.
Rational
Such a sum is always irrational.
If it says "negative irrational", then obviously it is irrational.
No