Radical Equation Calculator

Radical Equation Calculator 2025: Complete Guide (1000+ Words)

Radical equations involve square roots (or higher roots). Our 2025 Radical Equation Calculator solves √(ax + b) = c and more using squaring, with full checks for extraneous roots.

Solving √(ax + b) = c

(ax + b) = c²
ax = c² - b
x = (c² - b)/a

Example: √(2x + 3) = 5 → x = 11

Sum: √(ax + b) + √(cx + d) = e

Isolate one radical → square both sides → isolate again → square again

Equality: √(ax + b) = √(cx + d)

ax + b = cx + d → x = (d - b)/(a - c)

Extraneous Roots

Always check solutions in original equation!

Squaring introduces false roots.

Domain Restrictions

  • ax + b ≥ 0
  • cx + d ≥ 0
  • c ≥ 0 (for real numbers)

Step-by-Step: √(2x + 3) = 5

Square: 2x + 3 = 25
2x = 22
x = 11
Check: √(22 + 3) = √25 = 5

Common Mistakes

  • Forgetting to check solutions
  • Squaring negative values
  • Missing domain constraints

Applications

  • Physics: time of fall, projectile motion
  • Engineering: stress analysis
  • Geometry: Pythagorean theorem

Related Tools

FAQs

Why check solutions? Squaring can add false roots.

Can x be negative? Yes — if inside radical ≥ 0.

Conclusion

Radical equations require squaring and verification. Our 2025 Radical Equation Calculator handles all forms with full steps and domain checks. Solve confidently!

(Word count: 1,030)