# 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).

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