Simplifying Radicals Algebra 1 11-1

Radical Expressions – An expression that contains a square root Radicand – The expression under the square root sign Vocabulary

Properties

Use the prime factorization to break down the radicand Every pair of numbers that are the same can be removed and be one number on the outside Simplifying Radicals

Example

Variables can also be removed from under a radical sign Remove matching pairs (even number exponents) and express as half as many outside the radical sign Any result that has a odd exponent for a variable should be expressed as an absolute value Simplifying Radicals

Illustration Consider the following analogy Square root is a function. A lawn mower is a function. Illustration

Illustration Lawnmower Input is long grass Output is grass pieces Square Root Input is everything under the radical sign Output is everything outside the radical sign Illustration

Illustration Lawnmower Grass that goes through the function is smaller Square Root Numbers and variables that come through the function are smaller Illustration

Illustration Lawnmower Grass that does not go through the function, is left attached to the roots, typically this is shorter, never longer Square Root Numbers and variables that do not go through the function, are left inside the radical, and are typically smaller Illustration

Illustration Lawnmower If you run over short grass, it does not go through the function, and is unchanged Square Root Numbers and variables that cannot be reduced, do not go through the function and are unchanged Illustration

Example

When multiplying (dividing), the product (quotient) may allow further simplifying than the individual terms Simplifying Radicals

Example

Example

Example

Example

Practice

Rationalizing a Denominator – A simplified radical does not include any radical signs in the denominator. To remove denominator radicals, multiply the numerator and the denominator by the radical in the denominator Simplifying Radicals

Example

Example

Summary

Simplify each radical expression Review Problems

Simplify each radical expression Review Problems

Simplify each radical expression Review Problems

Simplify each radical expression Review Problems

Simplify each radical expression Review Problems

Simplify each radical expression Review Problems

Simplify each radical expression Review Problems

Simplify each radical expression Review Problems

Simplify each radical expression Review Problems

Simplify each radical expression Review Problems

Simplify each radical expression Review Problems

Pages 582 – 583 57 – 71 all, 76, 83 Homework