Mathematics » Introducing Decimals » Simplify and Use Square Roots

# Approximating Square Roots with a Calculator

## Approximating 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 $$\sqrt{\phantom{0}}$$ or $$\sqrt{x}$$ 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 $$\approx$$ and it is read approximately.

Suppose your calculator has a $$\text{10-digit}$$ display. Using it to find the square root of $$5$$ will give $$2.236067977.$$ This is the approximate square root of $$5.$$ When we report the answer, we should use the “approximately equal to” sign instead of an equal sign.

$$\sqrt{5}\approx 2.236067978$$

You will seldom use this many digits for applications in algebra. So, if you wanted to round $$\sqrt{5}$$ to two decimal places, you would write

$$\sqrt{5}\approx 2.24$$

How do we know these values are approximations and not the exact values? Look at what happens when we square them.

$$\begin{array}{ccc}\hfill {2.236067978}^{2}& =& 5.000000002\hfill \\ \hfill {2.24}^{2}& =& 5.0176\hfill \end{array}$$

The squares are close, but not exactly equal, to $$5.$$

## Example

Round $$\sqrt{17}$$ to two decimal places using a calculator.

### Solution

 $$\sqrt{17}$$ Use the calculator square root key. $$4.123105626$$ Round to two decimal places. $$4.12$$ $$\sqrt{17}\approx 4.12$$