Radical & Rational Equations Practice
Isolate, power, and — always — check. Solve radical and rational equations while hunting extraneous roots.
1 Practice
Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss earns another hint; a third miss walks you through the full solution.
2 What you’ll practice
Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.
Isolate and square
√(ax+b) = c → x.
Cube roots
∛(ax+b) = c.
Spot the extraneous
Which candidate fails?
No solution
Root = negative → impossible.
Rational equations
LCD then reject bad values.
Forbidden values
x = a zeroes it → no solution.
3 Watch out for these
The three mistakes students make most often on these problems.
√(x+5) = x−1 gives x = −1 too — but it fails the original.
√x + 3 = 7 → isolate √x = 4 FIRST, then square.
x = 3 zeroes the denominator in x/(x−3) = 3/(x−3) — reject it.