SOLUTION: prove that: 7-2 root 3 is an irrational number

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Question 779713: prove that: 7-2 root 3 is an irrational number
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Theorem 1: The square root of any non-negative integer that is not a perfect square is irrational.

Theorem 2: The product of a rational number and an irrational number is irrational.

Theorem 3: The sum of a rational number and an irrational number is irrational.

is irrational by Theorem 1.

is an integer and therefore rational by definition.

is irrational by Theorem 2.

is an integer and therefore rational by definition.

is irrational by Theorem 3.

John

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