Find the square root without using a calculator.

Question

Quizplus · Accepted Answer

First, estimate the square root by finding the perfect squares closest to 11: 9 and 16. Since 11 is closer to 9, we know that the square root of 11 is slightly greater than 3. Next, estimate the tenths place by dividing the remainder (2) by twice the whole number estimate (6). This gives 0.33, which means the square root of 11 is about 3.3. Finally, estimate the hundredths place by dividing the remainder (2) by twice the previous estimate (3.3). This gives 0.15, so the square root of 11 is about 3.15. Since none of the answer choices are above 3, we must estimate to the nearest tenth, giving us E) 0.2 (which is equivalent to 3.2).

Find the Square Root Without Using a Calculator