mathlib documentation

data.​rat.​sqrt

data.​rat.​sqrt

source
rat.​exists_mul_self
rat.​sqrt
rat.​sqrt_eq
rat.​sqrt_nonneg

Square root on rational numbers

This file defines the square root function on rational numbers, rat.sqrt and proves several theorems about it.

source
def rat.​sqrt  :
ℚ → ℚ

Square root function on rational numbers, defined by taking the (integer) square root of the numerator and the square root (on natural numbers) of the denominator.

Equations
source
theorem rat.​sqrt_eq (q : ℚ) :
rat.sqrt (q * q) = abs q

source
theorem rat.​exists_mul_self (x : ℚ) :
(∃ (q : ℚ), q * q = x) ↔ rat.sqrt x * rat.sqrt x = x

source
theorem rat.​sqrt_nonneg (q : ℚ) :
0 ≤ rat.sqrt q

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