Expert: Richard J. Raridon - 6/21/2006

Question
How would you explain square roots, cube roots, nth roots, and radicals to a student who is having difficulty understanding these concepts? What are some limitations of square root?  

Answer
If you have a number, then there are two equal numbers which, when multiplied together to give that number, they are call square roots.  For example, 25 can be obtained by multiplying 5*5 or (-5)(-5).  So 25 has two square roots, 5 and -5.  
For cube roots, three equal numbers are multiplied together.  For example, 2*2*2 = 8 so 2 is the cube root of 8.  
for nth roots, n numbers are multiplied together.  For example, the 10th roots of 1024 are 2 and -2.  
A radical often refers to a square root and can be written x^1/2.  A cube root would be x^1/3, etc.  
You can't take a square root of a negative number.  You can take the cube root of a negative number.  For example, (-8)^1/3 = -2