Question

(5√3-√27)^2
How do you prove this is an integer?

Answer 1

Expand the square. Remember that

(a - b)² = a² - 2ab + b²

With a = 5√3 and b = √27, we have

(5√3 - √27)² = (5√3)² - 2 (5√3) √27 + (√27)²

… = 25•3 - 10√81 + 27

… = 75 - 10√(9²) + 27

… = 102 - 10•9

… = 102 - 90

… = 12