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+ 7.1 Simplifying Radical Expressions
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+Warm Up #2
+HW Check – Exponents Practice
+
7.1 Simplifying Radical Expressions
+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.
+
+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
+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.
+Variable Examples:For variables you take GROUPS of the index out, leaving the remainder in!
+Simplify : 1.
2.
+3.
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+5.
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+7.
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+10.
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+Warm Up
+
Section 7.2
Multiplying & Dividing Radicals
+Multiplying Radical Expressions
If they are real numbers, then
+Examples:
1.
2.
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3.
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5.
6.
+Dividing Radical Expressions
+Examples:
1. 2.
+Rationalizing the Denominator
**Multiply the numerator and denominator by the denominator**
Then Simplify
Example: 1. No square roots in the denominator!
+
2.
3.
+Warm Up #3
+HW Check – 7.2 Odds
+
7.3Adding, Subtracting, Multiplying and Dividing Binomial Radical Expressions
+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*
+Like Radicals are radical expressions that have the same index and the same radicand.
xx 23
+
Like Radicals Unlike Radicals
= =
+Examples:
1.
2.
2624
425257
+3.
4.
5.
6.
55363
7875
2726
28 xx
+Always simplify radicals before combining!1. 2.
+3.
4.
5.
+Multiplying Binomials
To multiply, USE FOIL!
Example 1:
+
2.3. )31)(31(
+Dividing Binomial Radicals
To divide, Rationalize the denominator!(a + b)( a - b) = a2 – b2
These are called conjugates! They make radicals disappear!
+Examples:
1.
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2.
+Examples:
1.
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7.4 Rational Exponents
+Rational Exponents
+
Rational Exponents are another way to write radicals.
+Simplify each expression.
1.
2.
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4. 5.
+
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+Rational Exponents to Radicals
The Denominator is the INDEXThe Numerator is the POWER
+Converting to Radical Form
1.
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3. 4. 5.
+Converting to Exponential Form
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3. 4. 5.
+
Properties of Exponents also apply to Rational Exponents!
Write in Radical Form:
+2.
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+Simplify each expression.
1.
2.
+
3.
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+Warm Up #4
+HW Check – 7.4
+
7.5 Solving Radical Equations
+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?
+We use inverse operations to solve equations.
Solve: X2 = 4
+What is the inverse of cubing x?
Solve: X3 = 64
+Solve the following. Check your solutions!1. 2.
+6.
+
Solve
(x)1/2 = 3
**To solve radical equations with rational exponents,
raise each side to the reciprocal exponent!
+Examples:
1. 2.
+Solve
3. 4.
+
1.
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3. 4.
+You can also solve by graphing!
Given:
The equation is already equal to zero!
y=
Find the x-intercept!
