# Solve by taking square roots

- Square Roots Calculator
- Squares and Square Roots
- How to Solve Quadratic Equations using the Square Root Method

## Square Roots Calculator

Learn how to solve quadratic equations like x^2=36 or (x-2)^2=

fullWe think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you! Published by Rosaline Jacobs Modified over 3 years ago. Get x 2 or binomial squared by itself 2.

Let's take another look at that last problem on the previous page:. On the previous page, I'd solved this quadratic equation by factoring the difference of squares on the left-hand side of the equation, and then setting each factor equal to zero, etc, etc. I can also try isolating the squared-variable term on the left-hand side of the equation that is, I can try getting the x 2 term by itself on one side of the "equals" sign , by moving the numerical part that is, the 4 over to the right-hand side, like this:. Solving by Taking Square Roots. When I'm solving an equation, I know that I can do whatever I like to that equation as long as I do the exact same thing to both sides of that equation. On the left-hand side of this particular equation, I have an x 2 , and I want a plain old x. To turn the x 2 into an x , I can take the square root of each side of the equation, like this:.

That implies no presence of any x term being raised to the first power somewhere in the equation. Then solve the values of x by taking the square roots of both sides of the equation. I will leave it to you to verify. This problem is very similar to the previous example. My approach is to collect all the squared terms of x to the left side, and combine all the constants to the right side. The two parentheses should not bother you at all.

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Solving quadratics by taking square roots.

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If the square of x is 9, then x can be the positive or negative square root of All we need to do is remember to keep both the positive and negative square roots. Sometimes after taking the square root, though, we need to do a little more work. Put your back into it. In other words, we're taking the square root of both sides to knock out that exponent. Now we need to solve two equations.

## Squares and Square Roots

Solving Quadratic Equations with the Square Root Method, part 1 5-6a

## How to Solve Quadratic Equations using the Square Root Method

A quadratic equation can be solved by taking the square root of both sides of the equation. This method uses the square root property, Before taking the square root, the equation must be arranged with the x2 term isolated on the left- hand side of the equation and its coefficient reduced to 1. There are four steps in solving quadratic equations by this method: Step 1: Isolate the and terms. Use the addition and subtraction and isolate the and terms on the left-hand side of the equation. Then, use the multiplication and division axioms to eliminate the coefficient from the term. Step 2: Make the coefficient on the term equal to. Use multiplication or division to eliminate the coefficient from the term.

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Sal solves the equation 2x^2+3=75 by isolating x^2 and taking the square root of both sides.

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Put the Equation Into the Proper Form

Squares and Square Roots Taking Square Roots