Estimating and Approximating Square Roots
Learning Outcomes
- Estimate a square root that is not a perfect square
- Approximate square roots with a calculator
So far we have only worked with square roots of perfect squares. The square roots of other numbers are not whole numbers.

example
Estimate between two consecutive whole numbers. Solution Think of the perfect squares closest to . Make a small table of these perfect squares and their squares roots.
try it
[ohm_question]146633[/ohm_question]Approximate Square Roots with a Calculator
There are mathematical methods to approximate square roots, but it is much more convenient to use a calculator to find square roots. Find the or key on your calculator. You will to use this key to approximate square roots. When you use your calculator to find the square root of a number that is not a perfect square, the answer that you see is not the exact number. It is an approximation, to the number of digits shown on your calculator’s display. The symbol for an approximation is and it is read approximately. Suppose your calculator has a display. Using it to find the square root of will give . This is the approximate square root of . When we report the answer, we should use the "approximately equal to" sign instead of an equal sign. You will seldom use this many digits for applications in algebra. So, if you wanted to round to two decimal places, you would write How do we know these values are approximations and not the exact values? Look at what happens when we square them. The squares are close, but not exactly equal, to .example
Round to two decimal places using a calculator.Answer: Solution
Use the calculator square root key. | |
Round to two decimal places. | |