To find the number of different ways to arrange the letters of the word "SQUARE", we first note that the word consists of 6 distinct letters: S, Q, U, A, R, and E.
The formula to calculate the number of arrangements of \( n \) distinct objects is given by \( n! \) (n factorial), which is the product of all positive integers up to \( n \).
For the word "SQUARE", which has 6 letters, we calculate \( 6! \):
\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 \]
Calculating this step by step:
- \( 6 \times 5 = 30 \)
- \( 30 \times 4 = 120 \)
- \( 120 \times 3 = 360 \)
- \( 360 \times 2 = 720 \)
- \( 720 \times 1 = 720 \)
Thus, the total number of ways to arrange the letters of the word "SQUARE" is
\[ \boxed{720} \] ways.