# How to Estimate Negative and Positive Square Roots

A square root of a number \(n\) is a value that, when multiplied by itself, gives the number \(n\). Every positive real number has two square roots. One is positive, and the other is negative. For instance, the positive square root of \(9\) is \(3\) (because \(3\times3=9\)) and the negative square root is \(-3\) (because \(-3\times-3=9\)).

If the number is negative, it has no real square roots, only complex ones, because there's no real number that you can multiply by itself to get a negative number.

## A Step-by-step Guide to Estimating Negative and Positive Square Roots

Here is a step-by-step guide on how to estimate square roots:

**Positive Square Roots**

**Step 1:** Identify the number Let’s say you need to estimate the square root of a number, for instance, \(20\).

**Step 2:** Find two perfect squares it falls between The square root of \(20\) falls between the square roots of the perfect squares \(16\) \((4\times4)\) and \(25\) \((5\times5)\). So, \(4\) and \(5\) are our lower and upper estimates, respectively.

**Step 3**: Determine the closer square Is \(20\) closer to \(16\) or \(25\)? Since it’s closer to \(16\), we can say that the square root of \(20\) is slightly more than \(4\).

**Negative Square Roots**

The negative square root is simply the negative value of the positive square root. So, in our example, the positive square root of \(20\) was slightly more than \(4\), so the negative square root is slightly less than \(-4\).

For more precise estimations, you can use a calculator or mathematical software. Note that the method above only gives an approximate value. In reality, the square root of \(20\) is around \(4.47\) (for the positive root) and \(-4.47\) (for the negative root).

## Related to This Article

### More math articles

- 5th Grade MEAP Math Worksheets: FREE & Printable
- 5th Grade Georgia Milestones Assessment System Math Worksheets: FREE & Printable
- How to Find Unit Rates and Rates?
- Free GED Math Worksheets [Updated for 2023]
- 7th Grade MCAP Math Worksheets: FREE & Printable
- Intelligent Math Puzzle – Challenge 87
- How to Graph the Tangent Function?
- 4th Grade PARCC Math Practice Test Questions
- CBEST Math Worksheets: FREE & Printable
- FREE 5th Grade Georgia Milestones Assessment System Math Practice Test

## What people say about "How to Estimate Negative and Positive Square Roots - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.