$\sqrt{1.5625} = x$

Concept & Strategy When evaluating the square root of a decimal number, the number of decimal places in the result is exactly half the number of decimal places in the original perfect square. Step-by-Step Solution * **Calculation:** Disregard the decimal momentarily and focus on finding the square root of the integer $15625$. * Since the number ends in $25$, its square root must end in $5$. * The remaining part of the number is $156$. Find two consecutive integers whose product is $156$. We know $12 \times 13 = 156$. * Thus, the integer part of the square root is $12$, making the square root of $15625$ exactly $125$. * Re-insert the decimal point. The original number ($1.5625$) has 4 decimal places, so the root must have exactly 2 decimal places. * This gives $1.25$. Exam Strategy & Shortcut Check the last digit and the integer range. The number ends in $5$, so the root ends in $5$. The integer part is $1$, meaning the root is slightly greater than $1$. Test the boundaries: $1.2^2 = 1.44$ and $1.3^2 = 1.69$. Since $1.5625$ falls between them, the root must be $1.25$. Common Pitfall Incorrectly placing the decimal point in the final answer (e.g., answering $12.5$ instead of $1.25$). Remember that 4 decimal places under the root convert to 2 places outside the root. Final Answer **Therefore, the correct answer is 1.25.**