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In order to solve equations where a radical equals a constant, you first need to isolate the square root. From there, square both sides to "undo" the root, and solve for x. Once you have a solution(s), you'll need to check to make sure they're not extraneous. Any value of x that would make the radicand, or whatever is under the radical sign negative is outside of the domain, or extraneous. Here we'll see an example of a radical equation that has no solution.
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Concept (1)
Sample Problems (13)
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Solving an Equation with Radicals
Problem 1 4,413 viewsSolve:
4 ⋅ ∛x − 1 + 3 = 11 
Solving an Equation with Radicals
Problem 2 4,037 viewsSolve:
√x + 2 = x 
Solving an Equation with Radicals
Problem 3 3,669 viewsSolve:
√3x − 2 − √x + 3 = 1 
Solving an Equation with Radicals
Problem 4 200 views 
Solving an Equation with Radicals
Problem 5 194 views 
Solving an Equation with Radicals
Problem 6 191 views 
Solving an Equation with Radicals
Problem 7 189 views 
Solving an Equation with Radicals
Problem 8 185 views 
Solving an Equation with Radicals
Problem 9 179 views 
Solving an Equation with Radicals
Problem 10 185 views 
Solving an Equation with Radicals
Problem 11 180 views 
Solving an Equation with Radicals
Problem 12 177 views 
Solving an Equation with Radicals
Problem 13 185 views
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