How does a calculator know the answer?

Math and take root

What a root is in mathematics and how to pull the root is explained here in a simple way. Go to content:

  • A Explanationwhat you need roots for.
  • Examples how to calculate roots (also in writing, without a calculator).
  • Tasks / exercises to practice this yourself
  • A Video this topic.
  • A Question and answer area to this area.

Tip: You should already know what an equation and a power is. If you have no idea about this, please see solving equations and powers.

Explanation take root

We're looking at the basics of pulling the root here. But if you already know the basics, you are welcome to take a look at these topics (will be linked as soon as available):

  • Laws of roots / rules of roots
  • Root calculation
  • Roots with variables
  • Root equations

First of all, let's clarify why you need a root. A little hint: Whenever the school speaks of the root or pulling the root, it usually means the square root. Let's take a quick look at the definition, followed by examples:

Note:

The square root of a number a is the positive number that you have to square to get a.

The symbol for the root is this:

Example 1: Simple roots

Let's start with a few simple examples of how to pull the root. The root of 4 is simply 2, because 2 · 2 = 4. The root of 25 is 5, because 5 · 5 = 25. Here are four simple examples:

Let's look at a few more important terms. First of all, we have a root sign. You will find the radicand under the root sign. If you calculate the root you get the root value.

These were simple examples of how to pull the root. So we'll look at a slightly more difficult task in the next section.

Display:

Examples take root

How can one calculate the root? Well, in school and also during studies, the calculator is usually used. Alternatively, you can calculate the root without a calculator. Either through an approximation procedure or through the written root.

Example root of 2:

If you take the square root of 2 with the calculator you get this:

How do you get this result without a calculator? One possibility is to slowly approach the result through multiplications. We start like this for this example:

We want 2 as a solution. Therefore 1 is too small and 4 is too big. We therefore go in between once with 1.5 · 1.5.

The 2.25 is still bigger than 2. So let's try 1.4.

With the 1.96 we come very close to the 2. But are still below. So we don't try 1.4 but 1.41:

You can go on and on with this. One approaches more and more the 2 below the square root or the square root value 1.4142 ...

Note:

There are other written procedures for calculating roots. However, these are only dealt with marginally at school - if at all - and are therefore not explained here. With the approximation method, however, you can calculate the root once by hand. Alternatively, there is of course the pocket calculator.

Tasks / exercises root math

Show:

Video root

Explanation and examples

This video covers the basics of calculating the roots. Let's look at this:

  • What is a root in math?
  • Why do you need the calculation of the roots?
  • Simple examples are calculated.
  • Simple examples are explained.

Next video »

Questions with answers take root and root

In this section we look at typical questions with answers about root pulling.

Q: Are there any rules for root extraction?

A: Yeah, sure. As with pretty much anything in mathematics, there are rules in calculating the roots. However, these would blow up the article here. For this reason you can find them together with examples under Root Rules / Root Laws. There you also learn to simplify roots.

Q: is it possible to calculate roots in the head?

A: At least for simple root problems with square numbers everyone should be able to do this, especially for small numbers. You should know the roots of 2, 4, 9, 16 etc. by heart or calculate them quickly using knowledge of the multiplication table. If the roots are complicated, you should be able to roughly estimate what should be the result of the root. Otherwise, you can of course try to follow the written procedure for loosening roots in your head.

Q: Is there a root sign on the keyboard?

A: A normal keyboard does not have a symbol for a root. Various programs therefore offer the option of inserting the root symbol as a special character. \ Sqrt {} is used in latex.