Entire And Mixed Radicals Worksheet printable pdf download

Entire And Mixed Radicals Worksheet

Lesson 7 - Entire and Mixed Radicals

Specific Outcomes:

Express a radical as a mixed radical in simplest form (2.5).

Express a mixed radical as an entire radical (2.6).

Solve a problem that involves radicals (3.5).

Recall…

 Multiplication Property of Radicals:

��

√ ��

= √ ��

⋅ √ ��

where �� ∈ ��

��

√ ��

 Division Property of Radicals:

where �� > 0

√

��

√ ��

Investigate: Approximate the value of each radical to four decimal places.

a) √ 216

b) 2 √ 54

c) 3 √ 24

d) 6 √ 6

What do you notice?

Entire versus Mixed Radical:

Entire radical:

 The number is entirely under the radical sign in the form: √ ��

��

 e.g., √ 75, √ −28

, √ 352

Mixed Radical:

 A number written as a product of another number and a radical in the form: a √ ��

��

 e.g.,

6 √ 7, −3 √ 13

, 4 √ 99

Note: every mixed radical can be expressed as an entire radical. e.g., 2 √ 2 = √ 8

Converting Entire radicals to Mixed radicals, Using Prime Factorization:

Consider: √ 80

We can write the radicand 80, as a product of prime factors.

Entire And Mixed Radicals Worksheet