algebra1 adding and subtracting radical expressions
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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
CONFIDENTIAL 1
Algebra1Algebra1
Adding and Adding and SubtractingSubtracting
Radical ExpressionsRadical Expressions
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.
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
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.
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)
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.
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.
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.
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.
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.
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)
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.
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.
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
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)
CONFIDENTIAL 16
10) Find the perimeter of the trapezoid shown. Give your answer as a radical expression in simplest form.
10) 12√2 in
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
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.
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.
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.
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.
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.
CONFIDENTIAL 23
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