Why is the square root of a perfect square always rational?

In the polynomial below, what number should replace the question mark to produce a difference of squares? x2 + ? x - 36

Maria found the least common multiple of 6 and 15. her work is shown below. multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . multiples of 15: 15, 30, 45, 60, . . the least common multiple is 60. what is maria's error?

Solve the equation: x - 9 = -6 + 5 a. 21 b. 7 c. 14 d. 2