Help with Roots Of Real Numbers: Finding the Root

Finding Roots

What Is a Square Root?

Finding a square root is the opposite - or inverse - of squaring a number. For example, the square root of four is two, and two squared (2^2) is four. This can expressed by the following rule: If a^2 = b, then a = the square root of b. Square root problems can be solved using graphing calculators, but your teacher may not allow calculators on tests, so you will probably need to learn to solve them on your own.

Vocabulary Words

Below are a few definitions you will need as you start solving roots problems.

Real Numbers

Any number that can be found on a number line is considered a real number. This includes negative numbers, rational and irrational numbers.

Imaginary Numbers

A made-up number that you get by multiplying a real number by the symbol 'i'.

Radicand

The number that you are finding the square root of in an equation. For example, in the problem, 'Find the square root of 81' the radicand is 81.

Cheat Sheet

Finding the square roots of real numbers can be tricky, which is why most math teachers recommend that you memorize all of the roots up to 12. Most of the problems you'll encounter will use these roots, which are called perfect squares. Here's a quick cheat sheet:

square root (4) = 2

square root (9) = 3

square root (16) = 4

square root (25) = 5

square root (36) = 6

square root (49) = 7

Not-so-perfect Squares

If you're working with a larger number or one that is not a perfect square, you can figure out the answer through factoring. Simply break the number into prime factors.

For example, if you're trying to find the square root of 12, break 12 down to 2 x 2 x 3. Since there are two twos, you cross one out and move one outside the radical for a final answer of 2 square root (3). You can also get the answer by plugging radical 12 into your calculator and writing out the decimal.

Sample Problem

Find the square root of 20.

Begin by breaking 20 down into its prime factors: 2 x 2 x 5. Like the problem above, you can cross one of the twos out and move the other outside of the radical. The final answer is 2 square root (5).