algebra1 adding and subtracting radical expressions
DESCRIPTION
Algebra1 Adding and Subtracting Radical Expressions. Warm Up. Find the domain of each square-root function. 1) y = √(4x – 2) 2) y = -2√(x + 3) 3) y = 1 + √(x + 6). 1) exponential 2) quadratic. Adding and Subtracting Radical Expressions. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/1.jpg)
CONFIDENTIAL 1
Algebra1Algebra1
Adding and Adding and SubtractingSubtracting
Radical ExpressionsRadical Expressions
![Page 2: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/2.jpg)
CONFIDENTIAL 2
Warm UpWarm Up
1) exponential 2) quadratic
1) y = √(4x – 2)
2) y = -2√(x + 3)
3) y = 1 + √(x + 6)
Find the domain of each square-root function.
![Page 3: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/3.jpg)
CONFIDENTIAL 3
Adding and Subtracting Radical ExpressionsAdding and Subtracting Radical Expressions
Square-root expressions with the same radicand are examples of like radicals .
Like radicals can be combined by adding or subtracting. You can use the Distributive Property to show how this is done:
Notice that you can combine like radicals by adding or subtracting the numbers multiplied by the radical and
keeping the radical the same.
2√4 + 4√5 = √5(2 + 5) = 7√5
6√x - 2√x = √x(6 - 2) = 4√x
![Page 4: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/4.jpg)
CONFIDENTIAL 4
Adding and Subtracting Square-Root ExpressionsAdding and Subtracting Square-Root Expressions
A) 3√7 + 8√7 = √7(3 + 8) = 11√7
B) 9√y - √y = √y(9 - 1) = 8√y
C) 12√2 - 4√11 = √x(6 - 2) = 4√x
D) -8√(3d) + 6√(2d) + 10√(3d)= √(3d)(10 - 8) + 6√(2d) = 2√(3d) + 6√(2d)
Add or subtract.
√y = √y. The terms are like radicals.
The terms are like radicals.
The terms are unlike radicals. Do notcombine.
Identify like radicals.
Combine like radicals.
![Page 5: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/5.jpg)
CONFIDENTIAL 5
Now you try!
1a) -√71b) 3√31c) 8√n1d) √(2s) + 8√(5s)
Add or subtract.
1a) 5√7 - 6√7
1b) 8√3 - 5√3
1c) 4√n + 4√n
1d) √(2s) - √(5s) + 9 √(5s)
![Page 6: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/6.jpg)
CONFIDENTIAL 6
Sometimes radicals do not appear to be like until they are simplified. Simplify allradicals in an expression before trying to
identify like radicals.
![Page 7: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/7.jpg)
CONFIDENTIAL 7
Simplifying Before Adding or SubtractingSimplifying Before Adding or Subtracting
A) √(12) + √(27)
= √{(4)(3)} + √{(9)(3)}
= √4√3 + √9√3
= 2√3 + 3√3
= √3(2 + 3)
= 5√3
Add or subtract.
Factor the radicands using perfect squares.
Product Property of Square Roots
Simplify.
Combine like radicals.
![Page 8: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/8.jpg)
CONFIDENTIAL 8
B) 3√8 + √(45)
= 3√{(4)(2)} + √{(9)(5)}
= 3√4√2 + √9√5
= 3(2)√2 + 3√5
= 6√2 + 3√5
Factor the radicands using perfect squares.
Product Property of Square Roots
Simplify.
The terms are unlike radicals. Do not combine.
![Page 9: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/9.jpg)
CONFIDENTIAL 9
C) 5√(28x) - 8√(7x)
= 5√{(4)(7x)} - 8√(7x)
= 5√4√(7x) - 8√(7x)
= 5(2)√(7x) - 8 √(7x)
= 10√(7x) - 8 √(7x)
= 2√(7x)
Factor 28x using a perfect square.
Product Property of Square Roots
Simplify.
Combine like radicals.
![Page 10: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/10.jpg)
CONFIDENTIAL 10
D) √(125b) + 3√(20b) - √(45b)
= √{(25)(5b)} + 3√{(4)(5b)} - √{(9)(5b)}
= √(25)√(5b) + 3√4√(5b) - √9√(5b)
= 5√(5b) + 3(2)√(5b) - 3√(5b)
= 5√(5b) +6√(5b) - 3√(5b)
= 8√(5b)
Factor the radicands using perfect squares.
Product Property of Square Roots
Simplify.
Combine like radicals.
![Page 11: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/11.jpg)
CONFIDENTIAL 11
Now you try!
2a) 5√62b) 9√3 2c) 5√(3y)
Add or subtract.
2a) √(54) + √(24)
2b) 4√(27) - √(18)
2c) √(12y) + √(27y)
![Page 12: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/12.jpg)
CONFIDENTIAL 12
Geometry ApplicationGeometry Application
A) 12 + 5√7 + √(28)
= 12 + 5√7 + √{(4)(7)}
= 12 + 5√7 + √4√7
= 12 + 5√7 + 2√7
= 12 + 7√7
Write an expression for perimeter.
Product Property of Square Roots
Simplify.
Find the perimeter of the triangle. Give your answer as a radical expression in simplest form.
Combine like radicals.
Factor 28 using a perfect square.
The perimeter is (12 + 7√7) cm.
![Page 13: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/13.jpg)
CONFIDENTIAL 13
Now you try!
3 )10√b in.
3) Find the perimeter of a rectangle whose length is 2√b inches and whose width is 3√b inches. Give your answer
as a radical expression in simplest form.
![Page 14: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/14.jpg)
CONFIDENTIAL 14
Assessment
1) 14√3 - 6√3
2) 9√5 + √5
3) 6√2 + 5√2 - 15√2
1 )8√32 )10√53- )4√2
![Page 15: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/15.jpg)
CONFIDENTIAL 15
Simplify each expression. 4 )2√25 )17√36 )33√3
7( - )√5x)8 )2(√7c+)18√(6c)
9 )8(√2t-)4√(3t)
4) √(32) - √(8)
5) 4√(12) + √(75)
6) 2√3 + 5√(12) - 15√(27)
7) √(20x) - √(45x)
8) √(28c) + 9√(24c)
9) √(50t) - 2√(12t) + 3√(2t)
![Page 16: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/16.jpg)
CONFIDENTIAL 16
10) Find the perimeter of the trapezoid shown. Give your answer as a radical expression in simplest form.
10) 12√2 in
![Page 17: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/17.jpg)
CONFIDENTIAL 17
Adding and Subtracting Radical ExpressionsAdding and Subtracting Radical Expressions
Square-root expressions with the same radicand are examples of like radicals .
Like radicals can be combined by adding or subtracting. You can use the Distributive Property to show how this is done:
Notice that you can combine like radicals by adding or subtracting the numbers multiplied by the radical and
keeping the radical the same.
2√4 + 4√5 = √5(2 + 5) = 7√5
6√x - 2√x = √x(6 - 2) = 4√x
Let’s review
![Page 18: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/18.jpg)
CONFIDENTIAL 18
Adding and Subtracting Square-Root ExpressionsAdding and Subtracting Square-Root Expressions
A) 3√7 + 8√7 = √7(3 + 8) = 11√7
B) 9√y - √y = √y(9 - 1) = 8√y
C) 12√2 - 4√11 = √x(6 - 2) = 4√x
D) -8√(3d) + 6√(2d) + 10√(3d)= √(3d)(10 - 8) + 6√(2d) = 2√(3d) + 6√(2d)
Add or subtract.
√y = √y. The terms are like radicals.
The terms are like radicals.
The terms are unlike radicals. Do notcombine.
Identify like radicals.
Combine like radicals.
![Page 19: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/19.jpg)
CONFIDENTIAL 19
Sometimes radicals do not appear to be like until they are simplified. Simplify allradicals in an expression before trying to
identify like radicals.
![Page 20: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/20.jpg)
CONFIDENTIAL 20
Simplifying Before Adding or SubtractingSimplifying Before Adding or Subtracting
A) √(12) + √(27)
= √{(4)(3)} + √{(9)(3)}
= √4√3 + √9√3
= 2√3 + 3√3
= √3(2 + 3)
= 5√3
Add or subtract.
Factor the radicands using perfect squares.
Product Property of Square Roots
Simplify.
Combine like radicals.
![Page 21: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/21.jpg)
CONFIDENTIAL 21
C) 5√(28x) - 8√(7x)
= 5√{(4)(7x)} - 8√(7x)
= 5√4√(7x) - 8√(7x)
= 5(2)√(7x) - 8 √(7x)
= 10√(7x) - 8 √(7x)
= 2√(7x)
Factor 28x using a perfect square.
Product Property of Square Roots
Simplify.
Combine like radicals.
![Page 22: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/22.jpg)
CONFIDENTIAL 22
Geometry ApplicationGeometry Application
A) 12 + 5√7 + √(28)
= 12 + 5√7 + √{(4)(7)}
= 12 + 5√7 + √4√7
= 12 + 5√7 + 2√7
= 12 + 7√7
Write an expression for perimeter.
Product Property of Square Roots
Simplify.
Find the perimeter of the triangle. Give your answer as a radical expression in simplest form.
Combine like radicals.
Factor 28 using a perfect square.
The perimeter is (12 + 7√7) cm.
![Page 23: Algebra1 Adding and Subtracting Radical Expressions](https://reader036.vdocument.in/reader036/viewer/2022062422/568137f4550346895d9fb6db/html5/thumbnails/23.jpg)
CONFIDENTIAL 23
You did a great job You did a great job today!today!