Find the degree of the expressions: a)b)

 A radical expression contains a square root.  A radicand, the expression under the radical sign, is in simplest form if it contains no perfect square factors other than 1.  Using prime factorization we can simplify radical expressions. Radical or Square Root  Radicand

 X 2 = ______  16 = _______  49 = _______

 Examples: 1. 2.

3. 4.

 “Rational” means ratio of two integers, or fraction.  So a variable or number with a rational exponent will look like this….  So what does this have to do with radicals?

XY XY

XY XY 1 8 2

 So what would we do if we had a variable to the ¼ power?

 Why ¼ ? FORMULA:

 So radicals can be re-written as exponents! Re- write each one with a rational exponent… 1) 2) 3)

 Re-write each rational exponent as a radical… 4) 5) 6)

XY XY

 Why 2/3?

 Re-write each radical as a rational exponent… 1) 2) 3)

 Re-write each rational exponent as a radical… 4) 5) 6)

Example 1: Example 2:

Example 1: Example 2:

1: 2:

Example 1 (perfect square): Example 2 (with leftovers): Since this is a 3 rd root you find three in your “pairs” not just two!

1) 2)

1) 2)

Worksheet Bring in your Parent Forms!

Simplify. Write with a rational exponent Write in radical form, then simplify.

 In order to add/subtract radicals, the _____________ must be the same.  To add/subtract radicals, simply add/subtract the________________.

 Find the perimeter of the rectangle below in radical form:

 Find the perimeter of the square below in radical form:

 To multiply monomial radicals (radicals that only have one term), multiply their “outsides” together then multiply their “insides” together. Make sure you SIMPLIFY the radical!

 Don’t forget to simplify the product, when possible!

 Don’t forget to simplify the product, when possible.

 Find the area of the following triangle:

 How can we simplify these?

 We can never leave a radical in the denominator of a fraction.  In order to get rid of a radical in the denominator, we have to “rationalize” the denominator.  In other words, we need to get the “rat” (radical) out of the “den” (denominator).

 What operation cancels radicals?  What is ?

 Are we allowed to just randomly multiply the denominator by something?  What are we allowed to multiply by without changing the problem?

 Don’t forget to simplify your final answers!

 Don’t forget to simplify your final answers.

Worksheet