The negative sign outside of the radical means that our answer will be negative, but we don't really have to worry about that until the end. In particular, we want one of those factors to be a perfect square.

Unfortunately, 8 nor 3 are perfect squares, so we need to see if there is another way to simplify.

For example, is not a problem since (-2) • (-2) • (-2) = -8, making the answer -2.

In cube root problems, it is possible to multiply a negative value times itself three times and get a negative answer.

There simply is no way to multiply a number times itself and get a negative result. As research with imaginary numbers continued, it was discovered that they actually filled a gap in mathematics and served a useful purpose.

Imaginary numbers are essential to the study of sciences such as electricity, quantum mechanics, vibration analysis, and cartography.We first have to think of "what number squared is 4? Let's write it like this: Since 18 is not a perfect square, we must simplify this expression by rewriting it as a product of 2 square roots.We want to rewrite this so that one of the factors is a perfect square. Did you notice how we rewrote the square root of 18 as the product of 2 factors, and one of them was a perfect square?As soon as you see that you have a pair of factors or a perfect square, and that whatever remains will have nothing that can be pulled out of the radical, you've gone far enough.An equation that contains a radical expression is called a radical equation.In the first case, we're simplifying to find the one defined value for an expression.In the second case, we're looking for any and all values what will make the original equation true.That is, we find anything of which we've got a pair inside the radical, and we move one copy of it out front.When doing this, it can be helpful to use the fact that we can switch between the multiplication of roots and the root of a multiplication.This tucked-in number corresponds to the root that you're taking.For instance, relating cubing and cube-rooting, we have: ".

## Comments Solving Square Root Problems

## Learn How to Simplify a Square Root in 2 Easy Steps - Algebra Class

Learning how to simplify a square root can be broken down into 2 easy steps. You probably already know the answer to this problem, but let's break it down.…

## Simplify Squares Roots solutions, examples, videos

How to Simplify Squares Roots using perfect square method & prime factorization, examples and step by step solutions, How to simplify square roots by factoring.…

## Radicals Introduction & Simplification Purplemath

In either of two ways If we are doing a word problem and are trying to find, say, the. To simplify a term containing a square root, we "take out" anything that is a.…

## How to Solve a Square Root Equation - Sciencing

Dec 15, 2018. Problems involving square roots are indispensable in engineering, calculus and virtually every realm of the modern world. Although you can.…

## The Lost Art of Square Roots - Math Hacks - Medium

Jul 12, 2017. Ready to take a quick trip through the lost art of solving square roots. Note You needn't multiply 10•87² to solve the problem. I just did for.…

## Negative Value Under the Square Root Radical - MathBitsNotebook.

This square root problem is asking for a number multiplied times itself that. a square root first appeared, mathematicians thought that a solution did not exist.…

## The Basics of Square Roots Examples & Answers - Sciencing

Square roots are often found in math and science problems, and any student needs. The problem can be solved exactly using a calculator, and √8 = 2.8284.…

## Square Roots Calculator - Symbolab

Free Square Roots calculator - Find square roots of any number step-by-step. Middle School Math Solutions – Equation Calculator. Welcome to our new.…

## Solving Radical Equations

The second is that if the square root of any nonnegative number x is squared. Example. Problem. Solve. Add 3 to both sides to isolate the variable term on the.…

## Art of Problem Solving

Problem. Determine all real numbers $x$ which satisfy the inequality. for the first inner square root to be defined, and $x\geq -1$ for the second inner square.…