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SAT Math skill page

SAT Radical Equations Practice

Isolate the radical before squaring, then check every candidate in the original equation.

Practice radical equations in Dolphin SATPractice questions
12-18 min practice time3 questions on pageAdvanced Math
Practice time12-18 min
Practice questions3 questions
Best forAdvanced Math

What this tests

What to know for this SAT skill

Dolphin practice questions

Practice your skill

Question 1 of 3Easy
If square root of x = 7, what is x?
  1. 7
  2. 14
  3. 49
  4. 64
Show answer and solution
Correct answerC. 49

Solution walkthrough

  1. Square both sides to get x = 49.
Question 2 of 3Medium
If square root of (x + 4) = 6, what is x?
  1. 2
  2. 16
  3. 32
  4. 40
Show answer and solution
Correct answerC. 32

Solution walkthrough

  1. Square both sides: x + 4 = 36.
  2. Subtract 4 to get x = 32.
Question 3 of 3Hard
If square root of (x + 1) = x - 1, which value solves the equation?
  1. 0
  2. 1
  3. 2
  4. 3
Show answer and solution
Correct answerD. 3

Solution walkthrough

  1. Squaring gives x + 1 = (x - 1)^2, so x = 0 or x = 3.
  2. Checking the original rejects 0 because its right side is negative; 3 works.

Avoid these traps

Common mistakes on this skill

Squaring before isolating the radical

Move all non-radical terms away from the root first so the algebra stays manageable.

Forgetting to square an entire side

If a side contains multiple terms, square the complete expression rather than each term separately.

Keeping an extraneous solution

Squaring can create a candidate that does not satisfy the original equation, so every result must be checked.

Study plan

How to practice this skill in Dolphin

Dolphin Web gives you a personalized SAT study plan with lessons, unlimited Pip AI help, practice questions, full-length tests, and mistake review. The iPhone and Android apps are free. See plans.

  1. Isolate the radical expression.
  2. Square both complete sides of the equation.
  3. Solve the resulting equation and list every candidate.
  4. Substitute each candidate into the original radical equation.
Practice radical equations in Dolphin SAT

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FAQ

Questions about SAT Radical Equations Practice

Why can squaring create extraneous solutions?

Positive and negative values can have the same square, so squaring may erase a sign condition from the original equation.

Can I use a calculator on SAT radical equations?

Yes. The digital SAT lets you use a calculator on every Math question, including the Desmos graphing calculator built into the test. Radical equations are often faster by hand: isolate the radical, square both sides, and check each answer in the original equation.

How can Desmos help with SAT radical equations?

Graph each side as its own equation and look for where the graphs cross. For the square root of (x + 7) = x + 1, graph y = sqrt(x + 7) and y = x + 1. They cross only at x = 2. Squaring both sides also gives x = -3, but the graphs do not meet there because the square root of 4 is 2, not -2. A quick graph shows which answers are real solutions and which are extraneous.

What should I check before solving?

A principal square root is nonnegative, so the expression on the other side must also be nonnegative.