+ Warm Up #2. + HW Check – Exponents Practice + 7.1 Simplifying Radical Expressions.
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Transcript of + Warm Up #2. + HW Check – Exponents Practice + 7.1 Simplifying Radical Expressions.
![Page 1: + Warm Up #2. + HW Check – Exponents Practice + 7.1 Simplifying Radical Expressions.](https://reader036.fdocuments.in/reader036/viewer/2022062223/5a4d1b287f8b9ab059998049/html5/thumbnails/1.jpg)
+Warm Up #2
![Page 2: + Warm Up #2. + HW Check – Exponents Practice + 7.1 Simplifying Radical Expressions.](https://reader036.fdocuments.in/reader036/viewer/2022062223/5a4d1b287f8b9ab059998049/html5/thumbnails/2.jpg)
+HW Check – Exponents Practice
![Page 3: + Warm Up #2. + HW Check – Exponents Practice + 7.1 Simplifying Radical Expressions.](https://reader036.fdocuments.in/reader036/viewer/2022062223/5a4d1b287f8b9ab059998049/html5/thumbnails/3.jpg)
+
7.1 Simplifying Radical Expressions
![Page 4: + Warm Up #2. + HW Check – Exponents Practice + 7.1 Simplifying Radical Expressions.](https://reader036.fdocuments.in/reader036/viewer/2022062223/5a4d1b287f8b9ab059998049/html5/thumbnails/4.jpg)
+Nth Root
For any real number a and b, and any positive integer n, if an = b , then a is the nth root of b.
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+
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+Real Number Examples:Find the roots:1. Square Root of 4 Square Root of -4
2. Cube Root of 8 Cube Root of -8
Even Index, Negative Radican = No Real Solution
Odd Index, Negative Radican = Negative Solution
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+Simplifying Radical Numbers- Find the largest perfect square/cube factor.- Take the square/cube of the factor, goes on the
outside- Leftover factor stays INSIDE the radical.
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+Variable Examples:For variables you take GROUPS of the index out, leaving the remainder in!
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+Simplify : 1.
2.
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+3.
4.
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+5.
6.
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+7.
8.
9.
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+10.
11.
12.
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+Warm Up
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+
Section 7.2
Multiplying & Dividing Radicals
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+Multiplying Radical Expressions
If they are real numbers, then
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+Examples:
1.
2.
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+
3.
4.
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+
5.
6.
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+Dividing Radical Expressions
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+Examples:
1. 2.
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+Rationalizing the Denominator
**Multiply the numerator and denominator by the denominator**
Then Simplify
Example: 1. No square roots in the denominator!
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+
2.
3.
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+Warm Up #3
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+HW Check – 7.2 Odds
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+
7.3Adding, Subtracting, Multiplying and Dividing Binomial Radical Expressions
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+Adding Radical Expressions
Use the same concept as that of adding or subtracting like variables.
Example: 7 - 3x + 2x + 5
*Have to have like Terms to Add/Subtract*
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+Like Radicals are radical expressions that have the same index and the same radicand.
xx 23
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+
Like Radicals Unlike Radicals
= =
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+Examples:
1.
2.
2624
425257
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+3.
4.
5.
6.
55363
7875
2726
28 xx
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+Always simplify radicals before combining!1. 2.
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+3.
4.
5.
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+Multiplying Binomials
To multiply, USE FOIL!
Example 1:
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+
2.3. )31)(31(
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+Dividing Binomial Radicals
To divide, Rationalize the denominator!(a + b)( a - b) = a2 – b2
These are called conjugates! They make radicals disappear!
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+Examples:
1.
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+
2.
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+Examples:
1.
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+
2.
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+
3.
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+
4.
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+
7.4 Rational Exponents
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+Rational Exponents
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+
Rational Exponents are another way to write radicals.
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+Simplify each expression.
1.
2.
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+
3.
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+
4. 5.
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+
6.
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+Rational Exponents to Radicals
The Denominator is the INDEXThe Numerator is the POWER
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+Converting to Radical Form
1.
2.
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+
3. 4. 5.
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+Converting to Exponential Form
1.
2.
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+
3. 4. 5.
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+
Properties of Exponents also apply to Rational Exponents!
Write in Radical Form:
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+2.
3.
4.
5.
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+Simplify each expression.
1.
2.
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+
3.
4.
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+Warm Up #4
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+HW Check – 7.4
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+
7.5 Solving Radical Equations
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+Radical EquationsA radical equation is an equation that has a variable in a radicand or has a variable with a rational exponent.
Are these Radical Equations?
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+We use inverse operations to solve equations.
Solve: X2 = 4
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+What is the inverse of cubing x?
Solve: X3 = 64
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+Solve the following. Check your solutions!1. 2.
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+6.
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+
Solve
(x)1/2 = 3
**To solve radical equations with rational exponents,
raise each side to the reciprocal exponent!
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+Examples:
1. 2.
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+Solve
3. 4.
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+
1.
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+
3. 4.
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+You can also solve by graphing!
Given:
The equation is already equal to zero!
y=
Find the x-intercept!