Question

Prove √ 3 is irrational.

Answer #1

Prove that √ 3 is irrational.

Prove that the (square root of 3)/3 is irrational.

Prove that √3 is irrational. You may use the fact that n2 is
divisible by 3 only if n is divisible by 3.
Prove by contradiction that there is not a smallest positive
rational number.

Let x ∈ ℝ. Prove that if x is irrational, then 2 + x is
irrational

1. Prove that the sum of any rational number with an irrational
number must be irrational.
2. Prove or disprove: If a,b, and c are integers such that
a|(bc), then a|b or a|c.

Irrational Numbers
(a) Prove that for every rational number µ > 0, there exists
an irrational number λ > 0 satisfying λ < µ.
(b) Prove that between every two distinct rational numbers there
is at least one irrational number. (Hint: You may find (a)
useful)

Prove that for all real numbers x, if x 2 is irrational, then x
is irrational.

10. (a) Prove by contradiction that the sum of an irrational
number and a rational number must be irrational. (b) Prove that if
x is irrational, then −x is irrational. (c) Disprove: The sum of
any two positive irrational numbers is irrational

Prove that (17)^(1/3) is irrational. You may use the fact that
if n^3 is divisible by 17 then n is divisible by 17

Prove that the square root of 5 is irrational.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 14 minutes ago

asked 20 minutes ago

asked 20 minutes ago

asked 22 minutes ago

asked 26 minutes ago

asked 32 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago