Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or...
-
Upload
ilene-gallagher -
Category
Documents
-
view
222 -
download
0
Transcript of Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or...
![Page 1: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/1.jpg)
Let’s get Radical
The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root.
The expression under the radical sign is called the radicand.
Therefore: The square root of a negative number is not a real number.
No number squared equals a negative product. Example: √-25 has no real number solution.
However, , since the negative sign is outside the radical sign.
![Page 2: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/2.jpg)
![Page 3: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/3.jpg)
Quotient Property of Square Roots
![Page 4: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/4.jpg)
![Page 5: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/5.jpg)
Simplifying Square Roots
8
We can simplify if 8 contains a Perfect Square
![Page 6: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/6.jpg)
Simplifying Square Roots
8
4 2
2 2
Look to factor perfect squares (4, 9, 16, 25, 36…)
Put perfect squares in first radical and the other factor in 2nd.
Take square root of first radical
![Page 7: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/7.jpg)
Simplifying Square Roots
48
16 3
4 3
Factor any perfect squares (4, 9, 16, 25, x2, y6…)
(& Put perfect squares in first radical and other factor in 2nd)
Take square root of first radical
![Page 8: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/8.jpg)
Simplifying Square Roots
27x 2
9x 2 3
3x 3
Factor any perfect squares (4, 9, 16, 25, 36…)
(& Put perfect squares in first radical and other factor in 2nd)
Take square root of first radical
![Page 9: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/9.jpg)
Simplifying Radicals
100x 2 2x
Remember:
Factor any perfect squares (4, 9, 16, 25, 36…)
(& Put perfect squares in first radical and other factor in 2nd)
200x 3
![Page 10: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/10.jpg)
100x 2 2x
10x 2x
Take square root of first radical
200x 3 Simplifying Radicals
![Page 11: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/11.jpg)
Time for a“Mental Math”
Break!
![Page 12: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/12.jpg)
Welcome to“Make That Number”
![Page 13: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/13.jpg)
Using the numbers
5, 4, 8
in any order and any combination of multiplication, division, subtraction and/or addition, make the following
number:
12
![Page 14: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/14.jpg)
5 × 4 - 8
![Page 15: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/15.jpg)
Using the numbers
8, 6, 9 in any order and any combination of multiplication, division, subtraction and/or addition, make the following
number:
62
![Page 16: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/16.jpg)
8 + 6 × 9
![Page 17: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/17.jpg)
Now back to our regularly scheduled slideshow!
![Page 18: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/18.jpg)
Factor any perfect squares (4, 9, 16, 25, x2, y6…) from NUMERATOR & DENOM.
(& Put perfect squares in first radical and other factor in 2nd)
200x 3
25
Simplifying Fraction Radicals
100x 2 2x
10x 2x
25 5
200x 3
![Page 19: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/19.jpg)
Factor any perfect squares (4, 9, 16, 25, x2, y6…) from NUMERATOR & DENOM.
(& Put perfect squares in first radical and other factor in 2nd)
Take square root of first radical
200x 3
25
Simplifying Fraction Radicals
100x 2 2x
10x 2x
25 5
200x 3
10x 2x
5
![Page 20: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/20.jpg)
1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) from NUMERATOR & DENOM.
(& Put perfect squares in first radical and other factor in 2nd)
2. Take square root of first radical
3. REDUCE
200x 3
25
Simplifying Fraction Radicals
100x 2 2x
10x 2x
25 5
200x 3
10x 2x
5
2x 2x
![Page 21: Let’s get Radical The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root. The expression under the radical.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bfe41a28abf838cb58b6/html5/thumbnails/21.jpg)
Classwork/Homework
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.