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Isolate the Root First

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 26 of 43.

Squaring removes a root only when the root stands alone on its side. Try squaring √(x + 6) - 1 = 3 as it is. The left becomes (√(x + 6) - 1)^2, and a squared difference has a middle term: x + 6 - 2√(x + 6) + 1. The root is still there, and the equation is messier than before.

So get the root alone first. Move the 1 to the other side: √(x + 6) = 4. Now square both sides: x + 6 = 16, so x is 10. Check in the original: √(16) - 1 is 4 minus 1, which is 3.

The order is always the same: undo whatever is added to or subtracted from the root, square only when the root is alone, then check.

Challenge

Solve √(2x - 1) + 3 = 6. Get the root alone before you square.

Try it yourself

sqrt(2x - 1) + 3 = 6

Solve for x

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Radicals & Rational Exponents

1Simplifying Radicals

Roots and Powers Perfect Square Factors The Largest Square Letters Under the Root Cube Roots Recap: Simplifying Radicals

4Rationalizing

One Root Below A Number and a Root The Conjugate Below Recap: Rationalizing

7Powers and Roots Equations

Odd Powers Even Powers Fractional Powers Two Thirds Power Recap: Power Equations

2Adding & Subtracting Radicals

Like Radicals Simplify First Subtracting Recap: Adding Radicals

5Rational Exponents

One Over n m Over n Negative Exponents Exponent Rules Still Work Recap: Rational Exponents

8Radical Functions

Domain of a Root Evaluating Inverse of a Square Recap: Radical Functions

3Multiplying Radicals

Root Times Root Distributing a Root Two Brackets Conjugate Pairs Recap: Multiplying Radicals

6Radical Equations

Square Both SidesIsolate the Root FirstA False Answer Cube Root Equations Recap: Radical Equations

9Final Challenges

Final: Simplify and Add Final: Clear the Root Final: The Exponent Final: Check It Final: The Falling Ball