*Contributor: Erika Wargo. Lesson ID: 12824*

Rah rah rah! Go Squares! Sounds like a cheer for a geometry team! But square roots are important and useful in many areas. Learn the easy ways to dig up the square roots of numbers, then teach others!

categories

subject

Math

learning style

Visual

personality style

Otter

Grade Level

Middle School (6-8)

Lesson Type

Skill Sharpener

What is the square root of 4? Wait, squares have roots? I thought only trees had roots!

Squares don’t really have roots like a tree though, so what could it mean?

How do you solve for the square root of a number?

First, take a moment to review squares. A *square* is a shape whose length and width are equal. Look at the squares below. What multiplication fact can be made for each square? Discuss with a parent or teacher:

Did you notice that each multiplication fact included a number multiplied by itself? When a number is multiplied by itself, it is called “squaring a number.”

In Square 1, the multiplication fact was 2 x 2 = 4, Square 2 was 3 x 3 = 9, and Square 3 was 4 x 4 = 16. In math, the opposite of “squaring a number” is the “square root” of the number. A *square root* is a number that, when multiplied by itself, creates a given value. The square root symbol looks like this: √. It is called a "radical" and looks similar to a division bar symbol or a check mark. But they are not the same and do not mean the same thing!

To find the square root of a number, you can use grid paper or multiplication facts. Since you won’t always have grid paper, it is important to be able to use other methods to solve for square roots.

Here's your first square root problem to solve: Find the square root of 25, √25

**Method 1: grid paper**

Draw a square that has 25 total blocks. Since it is a square, the length and width are the same number. In order to get 25 blocks, you will need a length of 5 and a width of 5. 5 x 5 = 25. The square root of 25 is 5.

**Method 2: guess and multiply (multiplication facts)**

Think to yourself: What can we multiply by itself to get this number?

The number we are trying to get is 25. What number multiplies by itself to equal 25?

5 x 5 = 25, so the square root of 25 is 5.

**Method 3: calculator**

This method should be used for problems that cannot be easily solved with drawing a square or multiplication facts. On a calculator, find the square root button. It will look like the square root symbol, √ or ^{2}** √**. On most calculators, you will type in the value first, then press the square root button. In this problem, the square root of 25 is 5.

Some square roots will equal a whole number, but some will be decimal numbers. *Perfect squares* are the squares of whole numbers. If a number is not a perfect square, it will not equal a whole number answer. It is helpful to use a calculator when finding the square root of numbers that are not perfect squares.

**Example **Find the square root of 8, or √8.

A square cannot be drawn to represent 8 because there is no number multiplied by itself to equal 8.

Think of a number that would multiply by itself to get close to 8. Discuss with a parent or teacher.

One way to think about this problem would be to think backwards.

2 x 2 = 4 and 3 x 3 = 9. Since you need a number that multiplies by itself to equal 8, you should see that the square root of 8 will be in between 2 and 3.

Use a calculator to find the square root. Type in 8, square root symbol, and you will get a decimal answer. Round the number to two decimal places. √8 is about 2.82, which is less than 3.

Notice how a square model is used to represent squares and square roots as you watch MashUp Math's *What is a Square Root and a Perfect Square? | Common Core Math*:

After the video, discuss with a parent or teacher:

- How do you find the square root of a number?
- Which method of finding square roots do you think you will use?

In the *Got It?* section, you will practice finding the square roots of numbers as you complete interactive practice.