Lesson 1 Square and Square Roots Cubes and

Lesson 1 Square and Square Roots; Cubes and Cube Roots

Squares • The square of a number can be found by multiplying that number by itself. – Square the number 3: 3 x 3=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! 3 • Area: 3 Area= 3 x 3 or 32

Cube • Multiply that number by itself 3 times. – Cube the number 6: 6 x 6 x 6 – 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= 3 x 3 x 3 or 3 33 3 3

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) • Lets list all the perfect cubes from 1 -125! 1, 8, 27, 64, 125 (13, 23, 33, 43, 53) • What number is both a perfect square and cube?

Any questions so far?

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: - What is the value of 5 cubed? - What is the value of 2 squared? - What is the √ 16? - What is the √ 25? - What is the 3√ 64? - What number is a perfect square and a perfect cube? Show you know.

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… √ 17, √ 40, √ 72, √ 23

And your homework is…