Rational Exponents N.RN.2 – Rewrite expressions involving radicals and rational exponents using...
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Transcript of Rational Exponents N.RN.2 – Rewrite expressions involving radicals and rational exponents using...
Rational ExponentsN.RN.2 – Rewrite expressions involving radicals and rational
exponents using properties of exponents.N.RN.3 – Explain why the sum or product of two rational
numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero
rational number and an irrational number is irrational.
How to play…
• When a new problem is shown, write down your answer on a slip of paper (write it BIG)
• Do not show your answer to anyone!
• When the teacher says “SHOWDOWN” slap your answer down for everyone to see.
• Discuss your answers with your group, come to an agreement on the correct answer
Showdown
(-
… what is x?
Rational:
Integer:
Whole:
Natural:
Irrational:
Sets of Real Numbers
Always, Sometimes, Never
1. The sum of two rational numbers is rational2. The product of two rational numbers is a whole
number 3. The sum of a rational number and an irrational
number is rational4. The product of a nonzero rational number and
an irrational number is irrational
Always, Sometimes, Never
1. The sum of two rational numbers is rational (A)2. The product of two rational numbers is a whole
number (S)3. The sum of a rational number and an irrational
number is rational (N)4. The product of a nonzero rational number and
an irrational number is irrational (A)
Properties of ExponentsName Property Example
Product of Powers
Quotient of Powers
Power of a Product
Power of a Quotient
Power of a Power
Negative Exponent
The “nth” root of a
𝑛√𝑎RadicandIndex
Properties of RadicalsName Property Example
Radical of a Product
Radical of a Quotient
Radical of a Radical
Rational Exponents & RadicalsExponent Radical Example
or
Example 1. Example 2.
With your partner…Explain why it makes sense that and
Example 3: Simplify each expression. Express solutions in radical form (where necessary).
Example 4.
In parts B & C, you started with an expression in radical form, converted to rational exponent form, and then converted back to radical form. Explain the purpose of each conversion.
Example 5.
B) What is the simplified form of ? How is it related to ?
Example 6.
Example 6.
D)
E)
F)
Example 6.
G)
H)
Exit Card
1) A) B)
C) D)
2) What are rational and irrational numbers and
how are radicals related to rational exponents?