1. The problem is to find the square of 145, which means calculating $145^2$. 2. The formula for squaring a number $a$ is $a^2 = a \times a$. 3. Applying this to 145, we calculate $145^2 = 145 \times 145$. 4. Multiply 145 by 145: $$145 \times 145 = (100 + 40 + 5) \times (100 + 40 + 5)$$ 5. Use the distributive property: $$= 100 \times 100 + 100 \times 40 + 100 \times 5 + 40 \times 100 + 40 \times 40 + 40 \times 5 + 5 \times 100 + 5 \times 40 + 5 \times 5$$ 6. Calculate each term: $$= 10000 + 4000 + 500 + 4000 + 1600 + 200 + 500 + 200 + 25$$ 7. Sum all terms: $$= 10000 + 4000 + 4000 + 1600 + 500 + 500 + 200 + 200 + 25 = 21025$$ 8. Therefore, $145^2 = 21025$. Final answer: **21025**