Radical Equations
Key Questions

Answer:
A radical equation is any equation that involves any type of radical (square root, cube root, fourth root, et cetera).
Explanation:
Examples of radicals are:
#sqrt(46)# and#³sqrt(81)# . A radical equation is an equation that comprises one or more radicals. 
Let's start with an equation.
#x6=sqrtx# This can be solved easily by:
#x^212x+36=x# #x^213x+36=0# #(x9)(x4)=0# #x=9, x=4# but wait! we have to be careful whenever we square both sides of an equation.
Resubstitute the two answers into the original equation.
#96=sqrt9#
#3=3# That's fine, one more.
#46 = sqrt4#
#2 != 2# Our extraneous answer is
#x=4# To find the extraneous answer of any equation, just find the solutions and then resubstitute the solutions into the original equation. The answer that results in an illogical equation is the extraneous answer.

Use the facts (1) the cube of the cube root of an expression is equal to the expression and (2) cubing both sides of an equation yields an equivalent equation.
That is: (1)#(root(3)(a))^3=a# and (2)#a=b# if and only if#a^3=b^3# .(Note that point 2, above does NOT apply to squares. Squaring may introduce additional solutions. E.g. the only solution to
#x=3# is the obvious one. But#x^2=9# has two solutions.)Here's an example of you question:
Solve
#root(3)(2x+3)=5# .This equation is equivalent to (has the same solutions as):
#(root(3)(2x+3))^3=(5)^3# .Which simplifies to:
#2x+3=125#
And this is true exactly when#2x=122#
Which has only one solution:#61# .
(Or, if you insist, it has solution
#x=61# .) 
A radical equation is solved by simply squaring or cubing both sides of the equation. For example:
#√(2x+9)=5# #√(2x+9)^2# =#5^2# Then, continue to isolate the variable:
#2x+9=25# #2x+99=259# #(2x)/2=16/2# #x=8#
Questions
Radicals and Geometry Connections

Graphs of Square Root Functions

Simplification of Radical Expressions

Addition and Subtraction of Radicals

Multiplication and Division of Radicals

Radical Equations

Pythagorean Theorem and its Converse

Distance Formula

Midpoint Formula

Measures of Central Tendency and Dispersion

StemandLeaf Plots

BoxandWhisker Plots