Roots

Definition of Roots

• Roots in Mathematics are numbers that, when multiplied by themselves a certain amount of times, produce a given number.
• The square root of a number is a value that, when multiplied by itself, gives the original number.
• The cube root of a number is a value that, when multiplied by itself twice, gives the original number.

Identifying Roots

• To identify the square root of a number, look for a number which when multiplied by itself equals the given number. For example the square root of 25 is 5, because 5 x 5 = 25.
• To identify the cube root of a number, look for a number which when multiplied by itself twice equals the given number. For example the cube root of 27 is 3, because 3 x 3 x 3 = 27.

Calculating Roots

• The Square Root symbol is √. When you see “√25”, this means “the square root of 25”, which equals 5.
• Similarly, the Cube Root symbol is ³√. So “³√125” means “the cube root of 125”, which is 5.

Applications of Roots

• Roots are useful in various areas of mathematics, including algebra, geometry and trigonometry.
• They can be used to solve equations, simplify calculations and understand number patterns.

Common Misunderstandings with Roots

• Assuming that the root of a number always equals a whole number - this is not always the case. For example, the square root of 10 is a decimal (approximately 3.162).
• Confusing the square root and cube root symbols. Remember that the square root symbol is √, while the cube root symbol is ³√.
• Forgetting that every positive number has two square roots: a positive root and a negative root. For example, the square roots of 25 are 5 and -5.