Homework Solution lesson 8.5. Homework Lesson 8.7_page 533 #14-19 ALL.
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Transcript of Homework Solution lesson 8.5. Homework Lesson 8.7_page 533 #14-19 ALL.
Homework Solution lesson 8.5
9) X = 12
10)
11) n = 0
12) M = -3
13) Z = 8
14) T = 5
Homework
Lesson 8.7_page 533
#14-19 ALL
Lesson 8.7 Simplifying Radical Expressions
Properties of Radicals
For any real number a,
EXAMPLE:
Examples
√ 49𝑥2 𝑦5𝑚6Answer:
STRUCTURE
You can write an expression with rational exponent in radical form
Rewrite each expression in radical form
Radicals - definitions
The definition of is the number that when multiplied by itself 2 times is x.
x
2224 xxxx 2
16 8
Simplifying radicals
Most numbers are not perfect squares, but may have a factor(s) that is (are) a perfect square(s).
The perfect squares are:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100…
Simplify the radical expression by factoring out as many perfect squares as possible:
Simplifying radicals
The perfect cubes are:
1, 8, 27, 64, 125,…
Simplify the radical expression by factoring out as many perfect squares as possible:
Try these - simplify:
If a radical has a perfect square factor, then we can pull it out from under the sign.
Ex:
98724832
50 22525 25
745 bax
Warm-Up # Solve the equation by using the LCD. Check for
extraneous solutions.
Simplify
𝟐 𝒙𝒙+𝟑
−𝟏=𝒙
𝒙+𝟑
98
323
Homework Solution lesson 8.7
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Homework
Lesson 8.7 page 534
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Lesson 8.7
Adding, Subtracting, and Multiplying Radical Expressions
Combining like-terms
3x+2x – 2
(3+x) + (3 + x)
(4 + n) –(-1 -3x)
Adding or Subtracting Radicals
24232
24232182
To add or subtract square roots you must have like radicands (the number under the radical).
Sometimes you must simplify first:
TRY THESE:
5553
48753
)241()183(
)2431()66(
Multiplying Radicals
62343232
10152553
You can multiply any square roots together. Multiply any whole numbers together and then multiply the numbers under the radical and reduce.
TRY THESE:
10253
2261
)32)(123(
2
52
Warm-Up #
Simplify
Homework Solution lesson 8.7
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Homework
Lesson 8.7 page 533
#35-37 ALL
#82-84 ALL
Lesson 8.7
Dividing and Rationalizing Radical Expressions
Dividing RadicalsTo divide square roots, divide any whole numbers and then divide the radicals one of two ways:
1) divide the numbers under the radical sign and then take the root, OR
2) take the root and then divide. Be sure to simplify.
5
20
5
20 2
5
52
5
20 24
5
20 or
YOU TRY
4
110
40
4
10022
148
25
100
10
80
Converting Back and Forth
Convert from exponential to radical form:
Converting from radical to exponential:
Example
(64 𝑦7)13
3√𝑦 3
Rationalizing Radicals It is good practice to eliminate radicals from the denominator of
an expression. For example:
We do not want to change the value of the expression, so we need to multiply the fraction by 1. But “1” can be written in many ways…
2
3 2
222 2
21
2
23
22
23
2
2
2
3
We need to eliminate
Since we will multiply by one where
YOU TRY
3
5
15
2
10
53
23
35
83
52
120
72