Square and Square Roots;

Cubes and Cube Roots

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PeriodAssignment

Essential Question: What are perfect squares and cubes, what are their square and cube roots, and how do I find the root of a non-perfect square?

Study Questions: Notes:

Must ALWAYS have this heading!!

Squares

• The square of a number can be found by multiplying that number by itself. – Square the number 3: 3x3=9– Since the number 3 is multiplied twice, it is

written 32.

Why call it “Squared?”

• We call it squaring from the shape!– A square is unique because all 4 sides are the

same, so length and width are the same number.

– When we find the area, we are really multiplying a number by itself!

• Area: Area= 3x3 or 32 or 9

3

3

Cube

• Multiply that number by itself 3 times. – Cube the number 6: 6x6x6– It would be written 63

– Why cubed? Same idea as squared!• All sides of a cube are the same, so when we find

the volume, we multiply the same number 3 times.• Volume: Volume= 3x3x3

or

333

33

Perfect squares and Perfect cubes

• Lets list all the perfect squares from 1-100: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 (12,22,32, 42, 52, 62, 72, 82, 92, 102)

***you will need to know all the way to 225!

• Lets list all the perfect cubes from 1-125! 1, 8, 27, 64, 125 (13, 23, 33, 43, 53)

Study questions:

What are the perfect squares of 1-15?

What are the perfect cubes of 1-5?

Square root

• This is the inverse, or opposite, or squaring a number.– 32= 9 so √9 = 3

• A perfect square has a square root that is a whole number. – 9 is a perfect square because its square root

is a whole number, 3.– 10 is not a perfect square because its square

root is about 3.16, which is NOT a whole number.

Finding Square Root

What is the √16?

Think back to those perfect squares… what number squared is 16? 4! So… √16= 4

What is the √81?

What is the √36?

What is the 3√27?

Practice

• Let's practice what we just learned:

1. What is the value of 5 cubed?

2. What is the value of 2 squared?

3. √16=

4.√25=

5.3√64=

6.What number is a perfect square and a perfect cube? Show how you know.

Practice

• Let's practice what we just learned:

1. What is the value of 5 cubed? 125

2. What is the value of 2 squared? 4

3. √16=4

4.√25=5

5.3√64=4

6.What number is a perfect square and a perfect cube? Show how you know. 64!

8x8=64 4x4x4=64

Taking it a step further

What about those numbers that are not perfect squares? √17 for example?!

Lets go back to that list of perfect squares… what perfect squares is close to 17?

So we can estimate the √17 to be

between 4 and 5.

Let’s practice!

Estimate the square root of…

√40

√72

√23

Let’s practice!Estimate the square root of…

√40

We know √36 is 6 and √49 is 7, so √40

is BETWEEN 6 and 7

√72

We know √64 is 8 and √81 is 9, so √72

is BETWEEN 8 and 9

√23 We know √16 is 4 and √25 is 5, so √23

is BETWEEN 4 and 5

Study question:

How do you ESTIMATE the square root of a number that is NOT a

perfect square?

Summary

In 4-5 sentences, answer the essential question. Use some of these words:

• Perfect square

• Perfect cube

• Square root

• Cube root

• estimate