Radical Expressions

Operations on Radical Expressions• How can I simplify radical expressions?• How can I preform mathematical operations on

radical expressions?• How can I find the Geometric Mean between two

numbers?

Radical Expressions• Radical = square root symbol

• Perfect squares – multiply two numbers by themselves

• But life isn’t always perfect!

Radicals• Radical Expressions – an expression with a square

root

• Radicand – the expression under the radical sign

• We are going to simplify

Product Property• so….• If you just have a number under the square root• Step 1 – find the prime factorization of the number• Step 2 – find pairs of the same number• Step 3 – put the one from each pair in front of the radical

Radicands with numbers• Simplify:

Adding and Subtracting Radical Expressions• The radicand must be the same.

• Which expressions can be added to 3?

• 10• 10

Adding/Subtracting

Unlike Radicands• Simplify the radicands to see if they have like

radicands

Multiplying Radicals

• Step 1 – multiply the numbers• Step 2 – put the results under a square root• Step 3 – simplify as before

Multiplying Radicals• You can only multiply inside numbers with inside

numbers and outside numbers with outside numbers

Homework• Radical Quiz Friday!

• Worksheet

Quotient Property• so…

• but…

• NO RADICALS IN THE DENOMINATOR!

Rationalizing the Denominator

• Step 1 – multiply both the top and bottom of the fraction by the bottom

• Step 2 – the denominator will now be the number without a radical sign

• Step 3 – simplify the numerator, if possible

Rationalizing the Denominator• Simplify:

Geometric Mean• Geometric Mean – The geometric mean between

two numbers is the positive square root of their product.

• The two numbers are a and b, x is the geometric mean

• Use cross products and square roots

Examples• Find the geometric mean between each pair of

numbers:

1. 4 and 4

2. 4 and 63. 6 and 94. ½ and 2

Examples

Given the mean

Homework

• Worksheet• Radical Quiz Friday!