AIM: SWBAT find the square root or cube root of a number.
DO NOW:
1) State the first five Counting Numbers ______.
2) Whole Numbers are all the ______and ______.
3) Integers are all the ______and their ______.
4) ______are numbers that CAN be written as a fraction. Those would be
______decimals and ______decimals.
5) Give an example of a number that CANNOT be written as a fraction. ______
CLASSWORK:
______are numbers that CANNOT be written as a fraction. Those are
______, ______decimals.
Square – an operation – a number raised to the second power. A number times itself.
Ex: 42 = ______(-4)2 = ______-42 = ______
Perfect Squares – A number that is the square of an integer.
*****MEMORIZE THE FIRST 15 PERFECT SQUARES!*****
_____, _____, _____, _____, _____, _____, _____, _____, _____, _____, _____, _____, _____, _____, _____
Square Root – the opposite (inverse) of squaring a number.
- radical sign
“principal root” positive root
- negative root
Both the positive and negative roots
The number under the radical sign is called the “radicand”
4 is the radicand
The principal or (______) square root of 4 is ______
-The negative root of 4 is ______
±Both roots of 4 are ______and ______.
The square root of a perfect square is a RATIONAL Number.
The square root of a non-perfect square is an IRRATIONAL Number.
Find the SQUARE ROOT of each number.
1) = _____2) = _____3) - = _____
4) = _____5) = _____6) -= _____
7) = _____8) - = _____9) = _____
SQUARE each number.
10) 8 = _____11) 4 = _____12) -5 = _____
Cube – an operation – a number raised to the third power.
Perfect Cubes – A number that is the cube of an integer.
Cube Roots – the opposite (inverse) of cubing a number.
List the first 10 PERFECT CUBES.
______, ______, ______, ______, ______, ______, ______, ______,
______, ______
The cube root of a perfect cube is a RATIONAL Number.
The cube root of a non-perfect cube is an IRRATIONAL Number.
Evaluate.
1) = _____2) = _____3) =_____4) = _____
5) = _____6) = _____7) = _____8) = _____
Decide if each number is RATIONAL or IRRATIONAL.
9) ______
10) ______
11) -______
12) ______
13) ______
14) ______
15) ______
16) Why is it ok to have a negative number under the radical sign in a cube root, but not in a
square root?
HOMEWORK – SQUARES/PERFECT SQUARES & CUBES/PERFECT CUBES
List the first 15 PERFECT SQUARES.
______, ______, ______, ______, ______, ______, ______, ______,
______, ______, ______, ______, ______, ______, ______
List the first 10 PERFECT CUBES.
______, ______, ______, ______, ______, ______, ______, ______,
______, ______,
Evaluate.
1) = _____2) -= _____3) = _____4) -= _____
5) = _____6) = _____7) = _____8) = _____
SQUARE each number.
9) 7_____10) -5 _____11) 8 _____12) 15 _____
CUBE each number.
13) 7_____14) -5 _____15) 8 _____16) -10 _____
17) ______are numbers that CAN be written as a fraction. This would include ______decimals and ______decimals.
18) ______are numbers that CANNOT be written as a fraction. This would include ______, ______decimals.
Decide if each number is RATIONAL or IRRATIONAL.
19) ______20) ______
21) ______22) -______
23) ______24) ______
25) ______26) ______
AIM: SWBAT identify the two consecutive whole numbers between which the square root
of a non-perfect square lies AND round the answer to the nearest whole number.
DO NOW:
State whether the following numbers are RATIONAL or IRRATIONAL.
1) 2.1565656… ______2) -12 ______
3) ______4) 6.4851674… ______
5) List the first 15 perfect squares.
___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___
6) Use the number line below to graph the following: -2.5, -,, , , ,
-5 -4 -3 -2 -1 0 1 2 3 4 5
CLASSWORK:
Consider taking the “square root of 5”.
Can you think of a number, multiplied by itself that will equal 5? ______
Since 22 = 4 and 32 = 9, the answer must be a number in-between 2 and 3.
= 2.236067977499789696….
You will notice that the square root of a non-perfect square will ALWAYS be an IRRATIONAL NUMBER (a non-terminating, non-repeating decimal) so we will have to round our answers.
2 ( means approximate)
State the two consecutive whole numbers between which the square root lies.
1) _________2) _________
3) _________4) ___ ______
Find the SQUARE ROOT of each; round your answers to the nearest whole number.
5) ______6) ______
7) ______8) ______
SQUARE each number.
9) 12 ______10) 50______
11) 25 ______12) -20 ______
State the two consecutive whole numbers between which the square root lies.
13) ______14) ______
15) ______16)______
Find each square root. Round non-perfect squares to the nearest integer.
17) ______18) - ______
19) ______20) ______
21) - ______22) ______
23) State the problem numbers (#17-22) that are PERFECT SQUARES.
______
24) Use the number line below to graph the following: , -4, -,,-,
-5 -4 -3 -2 -1 0 1 2 3 4 5
HOMEWORK – SQAURE ROOTS – RATIONAL vs. IRRATIONAL
- Step 1 – Decide if the number is a “Perfect Square.” Answer yes or no.
- Step 2 – State whether the square root is Rational or Irrational.
- Step 3 – If the square root is Irrational then name the two consecutive whole numbers that the non-perfect square root lies between.
- Step 4 – Round the answer to the nearest whole number.
-Step 1- / -Step 2- / -Step 3- / -Step 4-
Perfect Square?
Yes or No / Rational or
Irrational / 2 Consecutive
Whole Numbers it
Lies Between / Rounded answer to
the nearest whole
number
EX: / No / Irrational / 2 and 3 / 3
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13) Use the number line below to graph the following: -, -2, 2.3, -, ,
-5 -4 -3 -2 -1 0 1 2 3 4 5
State whether the following numbers are RATIONAL or IRRATIONAL.
14) ______15) 0 ______
16) ______17) 0.242242224… ______
18) 2.17 ______19) ______
20) 24 ______21) -2______
22) ______23) ______
24) -______25) ______
Evaluate.
26) = _____27) -= _____28) = _____29) -= _____
30) = _____31) = _____32) = _____33) = _____
AIM: SWBAT simplify radical expressions.
DO NOW:
List the first 15 Perfect Square.
CLASSWORK:
When is a square root in simplest form?
When its radicand DOES NOT contain any perfect square factors other than 1.
There are two ways to simplify a radical expression:
Method 1:Find the largest perfect square that is a factor of that number.
Example: = = = 2
= 2
1) 2) 3) 4) 4
5) 6) 37) 8) 4
Method 2:Use its prime factorization to find all the perfect squares.
Example: = = = 2
9) 10) 11) 12)
HOMEWORK – SIMPLIFYING RADICALS
List the first 15 perfect squares.
___, ___, ___, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____ ,____ ,____
Simplify. You may use either method.
1) 2) 3) 4)
5) 6) 7) 8)
9) 10) 11) 12)
13) 14) 15) 16)
17) 18) 19) 520) 3
21) 422) 23) 24)
Aim: SWBAT Simplify Square Roots
Do Now:
Write each expression in simplest radical form.
1) 2) 3) 4)
Identify each number as RATIONAL or IRRATIONAL.
5) π ______6) ______
7) 0.47 ______8) 0. ______
9) 0.181181118… ______10) 0. ______
State ALL of the sets of numbers that each of the following belongs to.
11) 0 ______
12) -0. ______
13) 0.5678…. ______
14) 0.______
Answer each question with…
ALWAYSSOMETIMES NEVER
15) Counting Numbers are Whole Numbers.ASN
16) Rational Numbers are IrrationalASN
17) Integers are Whole NumbersASN
18) Rational Numbers are Real NumbersAS N
A square root is in simplest form when the radicand does not contain any perfect square factors other than one. To simplify a radical expression, find the largest perfect square that is a factor of that number.
1) 2) 3) 4)
Practice:
1) 2) 3)4)
5) 6) 7) 8)
Homework - Simplifying Radical Expressions
List the first 15 perfect squares starting with 1.
____, ____,____,____,____,____,____,____,____,____,
____,____,____,____,____,
Simplify each radical expression. Justify your answer.
1) 2)3)
4) 5) 6)
7) 8) 9)
10) 11)12)
Multiplying and Dividing with Square Roots
Aim: SWBAT express multiply and divide radical expressions.
Do Now: Write each of the following in simplest form.
1) 2) 3)
Multiplying Square Roots:
- Multiply the coefficients
- Multiply the radicands
- Simplify when necessary
Express each product in simplest radical form:
Example 1: Example 2:
Example 3: Example 4:
Dividing Square Roots:
- Divide the coefficients
- Divide the radicands
- Simplify when necessary (No square roots allowed in the denominator)
Example 1: Example 2:
Example 3: Example 4:
Square Roots to Memorize:
Homework:
1) ) ( )2) ) ( )3) ) ( )
4) 5) 6)
7) 8) 9)
10) Find the product of
Adding and Subtracting with Square Roots
Aim: SWBAT add and subtract radical expressions.
Do Now:
Find the area:
When we are adding and subtracting radicals, we need the radicals to be like radicals.
- Like radicals are radical expressions with the SAME radicand
- Ex. and are LIKE RADICALS
- When simplifying sums and differences you can combine the coefficients of the LIKE radical expressions.
1)9 + 7 = 2) 2 - 3 =
3) 4)
If the radicals are UNLIKE then try to simplify, first to see if there are like radicals.
5) 6)
If a radical expression with sums or differences contains UNLIKE radicals it is in simplest form.
7)
Let’s try some with mixed operations:
8) 9)
Homework:
1) 2) 3) 4)
5) 6) If is subtracted from ?7)
8) Find the perimeter:
AIM: SWBAT find the area & perimeter of geometric shapes.
DO NOW:
Find each sum or difference.
1) 2)
3) 4)
CLASSWORK:
Perimeter is the distance around the outside of a polygon. You find perimeter by adding up all the sides of a polygon.
Find the perimeter of each polygon. Show all work step-by–step.
1) 2)
3) 4)
Find the area of the following polygons:
5) 6)
7) Maggie is building rectangular dog run. She has determined the length will be feet and the width will be feet. Write an expression that Maggie can use to calculate how much fencing she needs for the perimeter of the dog run. (Draw a diagram)
8) Danielle is making a piece a modern art. She wants to paint a violet stripe around the edge of the square canvas. The edge of the canvas can be represented by . What is the perimeter of Danielle’s canvas? (Draw a diagram)
HOMEWORK – PERIMETER & AREA
1) Simplify the following expression:
2) Simplify:
3) Find the sum of and
4) Find the perimeter of a rectangle if the length is () and the width is
5) Find the perimeter of an equilateral triangle if each side is .
6) Find the perimeter of an isosceles triangle if the base measures and each of the other sides measures.
7) Find the perimeter of a square that has a side length of .
8) Find the area of a square that has a side length of .
9) SUBTRACTFROM
1