Example

Solving 9k2+1=0\sqrt{9k-2} + 1 = 0

Solve the radical equation 9k2+1=0\sqrt{9k - 2} + 1 = 0.

Step 1 — Isolate the radical. Subtract 11 from both sides:

9k2+11=01\sqrt{9k - 2} + 1 - 1 = 0 - 1

9k2=1\sqrt{9k - 2} = -1

The isolated square root equals 1-1, which is a negative number. Since the radical sign always denotes the principal (non-negative) square root, 9k20\sqrt{9k - 2} \geq 0 for every allowable value of kk. No real number substituted for kk can make the left side equal 1-1. Therefore, the equation has no solution.

This example demonstrates that when isolating the radical produces a negative value on the other side, the solving process stops immediately — there is no need to square both sides or perform any further algebraic steps.

0

1

Updated 2026-04-21

Contributors are:

Who are from:

Tags

OpenStax

Elementary Algebra @ OpenStax

Ch.9 Roots and Radicals - Elementary Algebra @ OpenStax

Algebra

Math

Prealgebra

Related
Learn After