Square Root Method
If x² = k then x = ±√k.
About this topic
If a quadratic has no x term, like x² = 25 or 2(x − 3)² = 18, isolate the squared part and take the square root of both sides. Remember the plus-or-minus sign, since both a positive and negative number square to the same result.
So x² = 25 gives x = ±5. If the squared expression is a binomial, as in 2(x − 3)² = 18, divide by 2 to get (x − 3)² = 9, take roots to get x − 3 = ±3, and then x = 6 or x = 0. If the number on the right is not a perfect square, leave the answer as a radical, such as x = ±√7, or approximate it with a calculator.
This method appears when finding the time for a dropped object to fall, since d = 16t² gives t = √(d/16), or when finding a side length of a square from its area. It also underlies the completing the square method and the quadratic formula.
Students often forget the negative root or take the square root of only one term, such as turning x² + 9 = 25 into x + 3 = 5. Isolate the square first. If the right side is negative, there are no real solutions.
Key ideas
- Isolate the squared term
- Take both roots
- Works when there is no x-term
Quick check
Use cases: where Square Root Method helps
- Homework: review the key idea behind Square Root Method before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Square Root Method without notes.
- Visual learning: play with the interactive lab to see how Square Root Method changes when you adjust its inputs.
- Teaching a friend: explain Square Root Method in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Square Root Method?
If x² = k then x = ±√k.
What will I learn in Square Root Method?
Isolate the squared term. Take both roots. Works when there is no x-term.
Is Square Root Method part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Square Root Method lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Square Root Method?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.