3-8 Semester Math 2 Simplifying radicals.

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Presentation transcript:

3-8 Semester Math 2 Simplifying radicals

Do now 3/9

Good Things

Agenda Do Now Good Things! Notes: Exponent Rules Simplifying Radicals Practice

Exponent Rules

Exponent Rules Simplify: (n2)3 Simplify: (x5)7 “Power to Power” Rule: multiply the exponents Simplify: (n2)3 Simplify: (x5)7

Exponent Rules Simplify: (x5)(x7) Multiplying Rule: add the exponents IF THEY HAVE LIKE BASES Simplify: (x5)(x7)

Exponent Rules

Exponent Rules

Your Turn! Take 3 minutes to do as many as you can before we review 4. (x-3) 6. 2. (x7)2 5. 3. (m6)(m2)

Simplifying radicals If the index is not written, it is automatically a 2

Perfect Squares 9 16 25 49 64 Today we will be working with numbers that are not perfect squares

Simplifying radicals 1. Write the prime factorization of the radicand (Factor tree) 2. Determine index of radical 3. Circle groups of numbers based on index and pull out ONE number from each group Ex: if index is 2, circle groups of 2 Ex: if index is 3, circle groups of 3 4. Leave anything not circled under the radical 5. Multiply numbers & variables outside the radical together

Prime factorization √75 5 15 2 8 5 3 2 4 5√3 2 2 2√2

Partner practice Simplify: √40 Simplify: √54

Spot the mistake Simplify: √18 Simplify: √18 2 9 3√2 2√3 2 9 3 3 3 3 One of these is done correctly. One of these is wrong. Turn and talk – identify which one is wrong and WHY it is wrong. Simplify: √18 Simplify: √18 2 2 9 9 3 3 3 3 3√2 2√3

Spot the mistake Simplify: √125 Simplify: √125 5 25 5√5 5 5 25 5 5 5 5 One of these is done correctly. One of these is wrong. Turn and talk – identify which one is wrong and WHY it is wrong. Simplify: √125 Simplify: √125 5 5 25 25 5 5 5 5 5√5 5

Switching Forms

Exponent Over Index cv cv cv

Exponent Over Index

Exponent Over Index

Partner Practice Front: Simplifying Radicals Back: Switching from radical to exponent form Solution station at the front!