Solving radical equations

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A radical equation is one in which one of the variables is under a radical.

To resolve a radical equation, do the following:

  • Step 1: Isolate the radical expression involving the variable. If more than one radical expression involves the variable, then isolate one of them.
  • Step 2: Raise both sides of the equation to the index of the radical.
  • Step 3: If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation.
  • Step 4: Check the answer in the original equation.


Solve $\sqrt{3x^2 + 10x} - 5 = 0$.



Isolate the radical part

$\sqrt{3x^2 + 10x} = 5$


Raise both sides to the index of the radical and square both sides.

Solving radical equations step 2


Apply the quadratic formula:

Solving radical equations step 3


Check the result:

Check the result

Then, we need to check the result for x = -5, so here’s what we get:


Answer: $x = -5 or x = \frac{5}{3}$.