Solve (√380.25 - ½)² - 11: Complete Square Root Expression

Since 380.25 is a decimal, look for a decimal that when squared gives 380.25. Try 19.5: $19.5 \times 19.5 = 380.25$. You can also recognize that $380.25 = \frac{1521}{4}$ and $\sqrt{\frac{1521}{4}} = \frac{39}{2} = 19.5$.

Because squaring doesn't distribute! $(a-b)^2 \neq a^2 - b^2$. Instead, $(a-b)^2 = a^2 - 2ab + b^2$. It's much easier to simplify inside the parentheses first, then square the result.

Check your fraction conversion! $\frac{1}{2} = 0.5$, so $19.5 - 0.5 = 19$ exactly. If you wrote 19.5 - 0.5 = 18.5, you made an arithmetic error in decimal subtraction.

Use PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). Always work from inside parentheses outward, then handle exponents, then other operations left to right.

Yes! Work backwards: if your answer is 350, then 350 + 11 = 361. Check if $\sqrt{361} = 19$, and if 19 + 0.5 = 19.5, and if $19.5^2 = 380.25$. This confirms your answer!