Radical Equations Flashcards

Which of the following is a radical equation?

What is the value of x if (8x-8)^(3/2)=64?

What is the value of x in squr x+11=15?

What is the value of x in squr 1-3x=x+3?

What are the possible values of x in x=2+squ x-2?

What is the solution for x in squr -3x-2=x+2?

What is the value of x in squr 2x+4=16?

What is the value of x in squr 4x+41=x+5?

What is the solution for x in 3squr x+8=-4?

What does (45-3x)^(1/2)=x-g yield for x?

What does SQUR x+10-1=x simplify to?

What is the value of x in squr x^2+81=x+10?

What height on the wall will a 15-foot ladder reach if it is placed 3.5 feet from the base?

Radical Equations Overview

Radical equations involve roots, typically expressed with variables under a radical sign.
Example: ( \sqrt{x} + 11 = 15 ).

Examples of Radical Equations

( 7\sqrt{x} = 14 ) is a fundamental radical equation.
( (8x-8)^{3/2} = 64 ) can be simplified to find ( x = 3 ).
For ( \sqrt{1-3x} = x + 3 ), the solution is ( x = -1 ).
The equation ( x = 2 + \sqrt{x-2} ) yields solutions ( x = 2 ) or ( x = 3 ).
In ( \sqrt{-3x-2} = x + 2 ), the solution is ( x = -6 ).

Advanced Radical Equations

( \sqrt{2x + 4} = 16 ) has the solution ( x = 126 ).
The equation ( \sqrt{4x + 41} = x + 5 ) gives ( x = -8 ).

Identifying Radical Equations

Determine if the equation contains a radical. Example: ( \sqrt{x} + 3 = 13 ).

Evaluating Complex Equations

For ( 3\sqrt{x} + 8 = -4 ), solving leads to ( x = -72 ).
The expression ( (45 - 3x)^{1/2} = x - g ) has a solution of ( x = 3 ).

Simplifying Radical Equations

The equation ( \sqrt{x + 10} - 1 = x ) can be rearranged to ( x + 10 = x^2 + 2x + 1 ).
In ( \sqrt{x^2 + 81} = x + 10 ), the rearrangement leads to ( x^2 + 81 = x^2 + 20x + 100 ).

Real-world Application

A 15-foot ladder placed 3.5 feet from a wall reaches a height of 14.6 feet according to the ladder height equation.

Repetition of Solutions

( \sqrt{-3x-2} = x + 2 ) repeats with ( x = -6 ) as its solution, emphasizing the importance of checking for extraneous roots.

Test your knowledge on radical equations and extraneous roots with these flashcards. Each card presents an equation or definition related to radicals, helping you to better understand this important mathematical concept.