Domains of Odd-Root and Even-Root Radical Functions

How would you explain to a seventh grader the difference between the domains of an odd root radical function and an even root radical function? How would you change your explanation for someone who had taken high school algebra?

Solution Preview

To a seventh grader, I would simply state that the domain of an odd root radical function is the ...

Solution Summary

We provide middle school and high school level explanations of the domains of odd-root and even-root radical functions.

Addition of radicals are treated similar to polynomials, but instead of multiples of x's and x2's, we have multiples of things that look very much like root x and root x - 2. When adding such expressions together, no arithmetic can be done underneath the radical. However, like radicals can be combined
together.
Question 1)

5 outside of the square root symbol then 3 under the square root symbol plus 15 outside of the square root symbol then 3 under the square root symbol plus 12 outside the square root symbol then 3 under the square root symbol plus 32.

Can you show me how to solve the following equations?
Square roots confuse me.
Sq Root of X-1=3?
Sq Root of X^3=8?
and ^3sq root of x^2=4?
Is the sq root of x^2=x an identity?

What law of radicals allows you to treat radical expressions as exponential expressions? How would you explain this to someone else and how would you explain adding like radicals? Include an example with your explanation. Use the following notation for square root: sqrt(3).

Discuss any difficulties you might have with grasping the concepts used in radical expressions. How would you explain square roots, cube roots, nth roots, andradicals to a student who is having difficulty understanding these concepts? What are some limitations of square root?

Find the square root. Assume that all of the variables represent positive real numbers.
1. The square root 25x^12
Find the cube root.
2. ^3 square root 512
Simplify the radical expressions. Assume that all variables represent positive real numbers.
3. the square root of 72 multiply the square root of 2
4. the square

1. If f(x)=2x-3 and g(x)=x2+1, find each of the following:
a) f(g(2))
b) g(f(3))
2. Let f(x)=x2+2 and g(x)=square root of 1-x2.
a) Find the domain and range of f and g.
b) Are the functions of f g and g f defined?
3. Given F(x)=cubed root of x+5, find functions f and g such that F=f g. Explain the answer.

** Please see the attached file for the complete problem description **
Express each radical in simple form, rationalize denominator, and perform the indicated operation
Show detailed step by step work!