5.7 Simplify and use square roots  (Page 3/8)

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.

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

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 $5.$

Simplify variable expressions with square roots

Expressions with square root that we have looked at so far have not had any variables. What happens when we have to find a square root of a variable expression?

Consider $\sqrt{9x^2},$ where $x\ge 0.$ Can you think of an expression whose square is $9x^2?$

When we use a variable in a square root expression, for our work, we will assume that the variable represents a non-negative number. In every example and exercise that follows, each variable in a square root expression is greater than or equal to zero.

Use square roots in applications

As you progress through your college courses, you’ll encounter several applications of square roots. Once again, if we use our strategy for applications, it will give us a plan for finding the answer!

Square roots and area

We have solved applications with area before. If we were given the length of the sides of a square, we could find its area by squaring the length of its sides. Now we can find the length of the sides of a square if we are given the area, by finding the square root of the area.

If the area of the square is $A$ square units, the length of a side is $\sqrt{A}$ units. See [link] .