# Radicals are in simplest form when:

## Presentation on theme: "Radicals are in simplest form when:"— Presentation transcript:

Radicals are in simplest form when:
No factor of the radicand is a perfect square other than 1. The radicand contains no fractions No radical appears in the denominator of a fraction

Perfect Squares 64 225 1 81 256 4 100 289 9 121 16 324 144 25 400 169 36 49 196 625

Multiplication property of square roots:
Division property of square roots:

Simplify = 2 = 4 = 5 This is a piece of cake! = 10 = 12

To Simplify Radicals you must make sure that you do not leave any perfect square factors under the radical sign. *Think of the factors of the radicand that are perfect squares. Perfect Square Factor * Other Factor = LEAVE IN RADICAL FORM =

Simplify = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = =

Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

If you cannot think of any factors that are perfect squares – prime factor the radicand to see if you have any repeated factors EX: 20 10 2 5

You can simplify radicals that have variables TOO!
= = = = =

Radicals are in simplest form when:
No factor of the radicand is a perfect square other than 1. The radicand contains no fractions No radical appears in the denominator of a fraction

REMEMBER THE PRODUCT PROPERTY OF SQUARE ROOTS:
Multiply Square Roots REMEMBER THE PRODUCT PROPERTY OF SQUARE ROOTS: OR

4 Multiply Square Roots To multiply square roots –
you multiply the radicands together then simplify EX: * = = 4 Simplify =

Try These : * * *

Let’s try some more:

Multiply Square Roots Multiply the coefficients Multiply the radicands

Multiply & Simplify Practice

Homework Practice 1. 2. 3. 4. 5.

Radicals are in simplest form when:
No factor of the radicand is a perfect square other than 1. The radicand contains no fractions No radical appears in the denominator of a fraction

Division property of square roots:

To simplify a radicand that contains a fraction –
first put a separate radical in the numerator and denominator Then simplify

Try These : Simplify:

If we have a radical left in the denominator then we must rationalize the denominator:
Since we cannot leave a radical in the denominator we must multiply both the numerator and the denominator by this radical to rationalize = = = = *

Hint – you will need to rationalize the denominator
Simplify: Hint – you will need to rationalize the denominator A. B. 4  C. D. 16

Simplify Radicals 1) 2) 3) 4)

Simplify some more: 5) 6) 7) 8)

Review writing in simplest radical form:
1) 2) 3) 4) 5) 6)

Review writing in simplest radical form:
7) 8) 9)

Which of the following is not a condition
of a radical expression in simplest form?  A. No radicals appear in the numerator of a fraction.  B. No radicands have perfect square factors other than 1.  C. No radicals appear in the denominator of a fraction.  D. No radicands contain fractions.