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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 SAT Try examples
12-18 min practice time 3 examples on page Advanced Math
Practice time 12-18 min
On-page examples 3 examples
Best for Advanced Math

What this tests

What to know for this SAT skill

Practice examples

Try a few SAT-style questions

Example 1 Easy

If square root of x = 7, what is x?

  1. 7
  2. 14
  3. 49
  4. 64
Show answer and explanation

Answer: 49

Square both sides to get x = 49.

Example 2 Medium

If square root of (x + 4) = 6, what is x?

  1. 2
  2. 16
  3. 32
  4. 40
Show answer and explanation

Answer: 32

Square both sides: x + 4 = 36. Subtract 4 to get x = 32.

Example 3 Hard

If square root of (x + 1) = x - 1, which value solves the equation?

  1. 0
  2. 1
  3. 2
  4. 3
Show answer and explanation

Answer: 3

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

Quick drills

Practice this skill from more angles

Drill 1

Isolate a square-root expression before squaring

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 2

Solve equations created by removing a radical

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 3

Recognize when squaring introduces an extra solution

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 4

Check candidate solutions in the original equation

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

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

  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

Related practice

Build the surrounding skills

SAT Rational Equations PracticeSAT Exponent Rules PracticeSAT Quadratic Equations PracticeSAT Math skill hub

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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.

Does the SAT test radical equations without a calculator?

Yes. The arithmetic is usually manageable when you isolate the radical and check the result systematically.

What should I check before solving?

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