## Square and Cube Roots

#### Aligned To Common Core Standard:

**Grade 8 Number System** - 8.EE.A.2

What are Square and Cube Roots? Your mathematics book is filled with squares and cube roots, isn’t it? But you do not have a clear idea about these concepts. Before you begin to comprehend what are square and cube roots, first you need to understand the underlying concepts in these terms. Both square and cube roots emerged from the concepts of square and cube. They are First, let’s take a look into what is a square and what is a cube?
**Square** - Squaring is as simple as multiplying a number by itself. Written as 32. The perfect squares are those of whole numbers. For instance; 1, 4, 9, 16, and so on.
**Square root** - Whereas the square root performs the exact inverse operation of squaring that number. Written as for example the square root of 36 is 6, which is obtained by finding the number which, when multiplied twice gives 36. In this case, it is 6.
**Cube** - Just like squaring, cubing is multiplying the same number thrice. Written as 53. The perfect cubes are 8, 27, 64, and so on.
**Cube root** - Cube root, on the other hand, goes the opposite direction. The cube root of 27 is 3, which means that when 3 multiplied thrice by itself makes 27.

### Printable Worksheets And Lessons

- Multiple Values For
Roots Step-by-Step Lesson- I show you how radicals start to
factor into this mix.

- Guided Lesson
- Using roots in equations, with fractions, and in word problems.

- Guided Lesson Explanation
- I find it helpful to draw pictures for word problems. That being
said, I forget to add one here.

- Independent Practice
- All the skills that we need to work on are here.

- Matching Worksheet
- There are only a few possible choices that make sense in these
problems. They are not close at all. Remember to round!

- Find the Square Root
Five Pack - You're given a whole number. Find each integers
square root.

- Simplify Square Roots
with Negative Numbers Five Pack - Simplify these in terms of
i. Why not throw an imaginary number in the mix?

- Square and Square Roots
Five Pack - I kind of got sick or using "X" and "Y".
So this made it more fun.

- Cube Roots Practice
Worksheet - Find the cubes and cube roots of small and large
integers.

- Writing Perfect Squares Five Pack - Make a perfect square. It is sometimes fun breaking apart numbers. It makes you into a mathematical hulk, of sorts!

#### Homework Sheets

Instead of just straight squares we make you work for it a bit.

- Homework 1 - Roots of a number are equal factors of the number itself.
- Homework 2 - We know the root number is an equal factor of the number.
- Homework 3 - What is the side length of a square with an area of 36 ft?

#### Practice Worksheets

Simplifying problems in terms of i was added to this section. I have seen this standard include that skill often.

- Practice 1 - Find the two values for √225. You will also slove basic algebra based problems.
- Practice 2 - You will work with some advanced skills on simplifying expressions in terms of i.
- Practice 3 - Leave your footprints on this one. You will need to reverse engineer a few of these.

#### Math Skill Quizzes

Each quiz covers a different skill within the standard.

- Quiz 1 - Find the two values for √2500. This is the type of exercise you can expect here.
- Quiz 2 - Solve for x
^{2}= 576. You will also solve home construction related word problems. - Quiz 3 - Simplify in terms of i (1/2)√920. Who doesn't want to do this right?
- Cube Root Quiz 4 - For questions 5 - 10 find the value of all the cube roots. You will begin by calculating end values.