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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