Simplifying Expressions
This is the equivalent of x^(1/2).
The square root of x.
The first step in solving √(x + 4) = 3.
Squaring both sides.
Forgetting to do this after solving an equation with a square root can lead to wrong answers.
Checking for extraneous solutions.
The simplified form of √(12x3).
2x√(3x).
The solution to (x + 1)^(1/2) = 4.
x = 15.
A common error when solving x^(2/3) = 4 is forgetting to do this to both sides.
Raise to the power of 3/2.
The rule that states (x^(a/b)) ^c equals this.
x^ (a*c/b).
To solve x^(2/3) = 9, raise both sides to this power
This mistake occurs when you incorrectly multiply exponents instead of adding them when using the product rule.
Applying the wrong exponent rule.
The rationalized form of 1/ square root of 3.
square root of 3/3.
The valid solution for √(x + 2) = x - 1 after checking for extraneous solutions.
x = 3.
Squaring both sides of an equation can lead to this issue.
Introducing extraneous solutions.
Converting x^(5/4) into radical form results in this.
The fourth root of x^5 or 4/(x^5).
When solving (x + 2)^(2/3) = 8, this is the simplified result after raising both sides to the power of 3/2.
x + 2 = 16.
When simplifying (3x^2)^(1/2), failing to correctly apply the exponent to both 3 and x results in this mistake.
Only taking the square root of x and not 3.