Square Roots and Cube Roots

In this chapter we’re going to be exploring square roots and cube roots. This is just a quick summary of what square roots and cube roots of a number are and how to find them on standard calculators.
Squared means “multiplied by itself” for example; m² = mxm. Square root is the reverse of this process. Square root means what number multiplied by itself provides the out outcome in question, from our example above √m² = m. m is the answer.

Example

Find the square of 49
The question also means find the √49 or 49^½. Both displays are used in mathematics especially each for different branches such as Calculus or Algebra.
The question is asking what number when multiplied by itself gives 49.
On a calculator it is much easier to find the answer. Most calculators have the square root button. To find the square root of 49 on the calculator you press.

When the above is pressed the outcome you shall get is 7. On the paper we write;

Square roots can be positive or negative. And when solving the problems you have to watch out for the signs. You must know that if you multiply a negative number by itself you get a positive number, such as;

But multiplying two positive numbers results in a positive number such as below;

This must mean that;

Cube roots

Cubed means number multiplied by itself three times, for example;

Cube root is the reverse process of the above; Cube root means what number multiplied by itself three times gives the number in question.

Example

Find the cube root of 64.
The question above can also be written as find the ∛64 or 64^1/3. Again both notations are popular in maths.
The question asks what number multiplied by itself three times gives 64.
You can find the cube root of 64 or ∛64 more easily on a calculator. To find this you press;

We can write this on paper as;