1.2 Multiply and Divide Radicals

I can multiply and divide radical expressions Essential standard I can multiply and divide radical expressions I can rationalize the denominator

SIMPLIFY RADICALS EXPRESSIONS 1) 𝑥 4 2) 49 𝑥 8 3) 5 32 𝑥 10 𝑦 15

SIMPLIFY RADICALS EXPRESSIONS 4) 27 5) 3 54 𝑎 3 𝑏 7 6) 54 𝑥 4 𝑦 5 𝑧 7 7) 60𝑥 𝑦 3

𝑛 𝑥 ⋅ 𝑛 𝑦 = 𝑛 𝑥⋅𝑦 MULTIPLYING RADICALS You can only multiply radicals with the same index. 𝑛 𝑥 ⋅ 𝑛 𝑦 = 𝑛 𝑥⋅𝑦

PROBLEM 1 Can you simplify the product of the radical expressions? Explain. A) 3 6 ⋅ 2 B) 3 −4 ⋅ 3 2

PROBLEM 2 What is the simplest form of 72 𝑥 3 𝑦 2 ⋅ 10𝑥 𝑦 3 ? Reminder: 𝑛 𝑥 ⋅ 𝑛 𝑦 = 𝑛 𝑥⋅𝑦

DIVIDING RADICAL EXPRESSIONS Much like multiplication, if two radicals have the same index you can divide the coefficients and divide the radicands. Then simplify. 𝑎⋅ 𝑛 𝑥 𝑏⋅ 𝑛 𝑦 = 𝑎 𝑏 ⋅ 𝑛 𝑥 𝑦

PROBLEM 3 What is the simplest form of the quotient? A) 18 𝑥 5 2 𝑥 3 B) 3 162 𝑦 5 3 3 𝑦 2

RATIONALIZE THE DENOMINATOR As long as you multiply a fraction’s numerator and denominator by the same number the value of the fraction does not change. We can use this to ‘rationalize the denominator’. 1 2 → 1 2 ⋅ 2 2 → 1⋅ 2 2 ⋅ 2 → 2 2

PROBLEM 4 Simplify by rationalizing the denominator. A.) 2 7

GOT IT? Simplify by rationalizing the denominator. 7𝑥 5

I can multiply and divide radical expressions Essential standard I can multiply and divide radical expressions I can rationalize the denominator