Square and Square Roots Cubes and Cube Roots
Square and Square Roots; Cubes and Cube Roots
Must ALWAYS have this heading!! First Name Last Name Date Period Assignment 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:
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 3 2 or 9
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) ***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 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 you know. 64! 8 x 8=64 4 x 4 x 4=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
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