Understanding Squares and Square Roots

Grade 8 Mathematics Mr. J. Lingley

1 Opposite OperationsIn class we have said that a square and a square root are opposite operations. This means that one cancels the other.

If that is true, then what would happen if we had a question that looked like this...

√162

1 Opposite Operations√162xx

Easy Explanation: They cancel each other out leaving the number as the answer.

Hard Explanation: 16 x 16 = 256. √256 = 16

Brings you back to the same spot.

* As a group of experts decide how you are going to explain this to your home group.

1 Expert Practice√82 √232

√52 √142

√22 √7892

√262 √122

Once you feel comfortable, with these questions, each person must be ready to explain the

concept to their home group.

2 Adding Roots/Subtracting #sThere is a pattern that emerges when we add square roots, and find the difference between two square roots that come after another.

√36 + √25 = 6 + 5 = 11

For example...

36 - 25 = 11

√81 + √64 = 9 + 8 = 17 81 - 64 = 17

2 Adding Roots/Subtracting #sHere’s what you need to do:

1. Choose two consecutive square numbers like:

16 and 25, 100 and 121, 121 and 144.

2. Find the sum of their square roots:

ex. √16 + √25 = 4 + 5 = 9

3. Find the difference, by putting

the largest number first: 25 - 16 = 9

4. Make sure all members of your expert group

understand how to explain this concept.

3 Ordering Squares and √sOne of the skills we will learn is how to complete is ordering whole numbers and square roots.

Ex: Order from least to greatest:

√36, 36, 4, √9

Least Greatest

6 3

3 4 6 36

3 Ordering Squares and √sAll you need to do is find the square roots first, then order the whole numbers.

3 Expert PracticeOrder from least to greatest.

√400, √100, 19, 15

√81, 81, √100, 11

√49, √49, √36, 9

Prepare your expert explanation for your home group.

4 Adding SquaresLet’s add some squares.

22 + 32

4 + 913

It’s simple. Let’s Try some more...

4 Expert PracticeLet’s add some squares.

32 + 42

52 + 62

72 + 82

92 + 102

112 + 122