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Without using a calculator how do you determine whether a RADICAL

represents a rational or an irrational number? Use examples to explain.

 Dec 2, 2020
 #1
avatar+115954 
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Prime factor the integer  under  the radical

 

Call  the  index of the radical, n

 

If  n  does not evenly divide  every  exponent in the prime factorization, then  we have an irrational result

 

Two examples

 

2√ 16  =   2√2^4      2 divides 4 evenly,,,so we have a rational answer  because   √16  = 4

 

3√ 32  =  3√ 2^5      since 3 does not evenly divide 5, we have an irrational answer  =  23√2^2  = 23√4

 

 

cool cool cool

 Dec 2, 2020
edited by CPhill  Dec 2, 2020
 #2
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thank u

mav002  Dec 2, 2020

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