Radicals Review

4 April 2011

Parts

72 Coefficient

Radical Sign

Radicand – the number underneath the radical

sign

Radical

Pronounced: 2 times the square root of 7 OR 2 radical 7

Simplest Radical Form

When you cannot factor any more perfect squares from the radicand The radical cannot be simplified further

We always want our answers to be in simplest radical form

24323

258

3

176

Getting Radicals into Simplest Radical Form1. Write the radicand as the product of

factors, where one (or more) factors is a perfect square

2. Take the square root of any perfect squares (Remember to multiply any coefficients in front of the radical sign!)

3. Repeat until you cannot factor any more perfect squares from the radicand

Tips for Getting Radicals into Simplest Radical Form Always check if the radicand is

perfect square! Check if factorable by common

perfect squares – 4, 9, 16, or 25 If the radicand is prime (or if its only

factors are prime), then it’s in simplest radical form

Be persistent! You don’t have to find the largest

perfect square the first time you factor the radicand

Examples 48

Examples2x1126

Examples9x1084

Your Turn:

Write problems 1 – 8 in simplest radical form.

Adding and Subtracting Radicals

You can only combine radicals with the same radicand (like radical terms)!

1. Rewrite all radicals in simplest radical form first!

2. Add or subtract the coefficients of like radical terms

Examples 5652

Examples 12382

Examples 20624105183

Your Turn:

For problems 9 − 12, simplify. Write the answer in simplest radical form.

Multiplying Radicals

Multiply like parts coefficients * coefficients radicand * radicand

Write answer in simplest radical form

Examples5x2x5x14

Examples 4x16x5

Examples )532)(51(

Your Turn:

13. 14.

15. 16.

What is rationalizing?

The process of algebraically removing a radical sign from one part of a fraction

We generally rationalize the denominator (But we can rationalize the numerator.)

Why rationalize? The result is easier

to estimate and understand

Also shows up in solving limits (in calculus) 2

2

2

1

Definitions

Monomial – An expression with exactly one term Example: 3y or –7x3

Binomial – An expression with exactly two terms Example: 6 + 4x or 10y4 – 8

Definitions, cont.

Conjugates – binomial expressions, such as (a + b) and (a – b), that differ only in the sign of the second term

Examples: (3 – x) and (3 + x) (4y5 + 2x2) and (4y5 – 2x2)

The product of conjugates is a2 – b2