ACT Preparation / Unit 7 ACT 0614 worked example, 60 to 90 seconds
Simplifying a Radical Expression
The idea
To simplify a radical expression, work in four steps. First, rewrite any rational exponents as radicals, or radicals as exponents, whichever makes the arithmetic easier. Second, factor each radicand and pull out perfect squares. Third, rationalize any denominator that still holds a radical. Fourth, combine like radicals.
In practice
Worked example: simplify √50 + √18 − 4/√2. Step two: √50 = 5√2 and √18 = 3√2. Step three: 4/√2 = 4√2/2 = 2√2. Step four: 5√2 + 3√2 − 2√2 = 6√2. Second: 12^(1/2) + √27. Step one: 12^(1/2) is √12. Step two: √12 = 2√3 and √27 = 3√3. Step four: 2√3 + 3√3 = 5√3.
Where people slip
Do not combine before simplifying. √50, √18 and 4/√2 look like three unlike terms, and each one turns out to be a multiple of √2.
Your place on the trail
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