Question

If a² = 7/36, then a is a) Rational b) irrational c) whole number d) integer

Answer 1

Answer:

a = + or - sqrt(7)/6, which are irrational ( Answer Choice (b) ) for either case.

Step-by-step explanation:

a^2 = 7/36 implies that

a^2 - 7/36 = 0, by subtracting 7/36 from both sides of the equation, which implies that

(a - sqrt(7)/6)(a + sqrt(7)/6) = 0, by factoring, which implies that

a - sqrt(7)/6 = 0  or  a + sqrt(7)/6 = 0, by the zero product property of the real number system, which implies that

a = sqrt(7)/6 or a = - sqrt(7)/6, which are both irrational, since sqrt(7) is irrational and an irrational number divided by an integer (other than 0) is irrational.