POWER AND ROOTS

Introduction

Powers are used when we want to multiply a number by itself repeatedly.

1.      Powers

When we wish to multiply a number by itself we use powers. For example, the quantity 74= 7 × 7 × 7 × 7 is usually written as 74. The number 4 tells us the number of sevens to be multiplied together. In this example, the exponent, or index, is 4. The number 7 is called the base. Example 62 = 6 · 6 = 36. We say that ‘6 squared is 36’, or ‘6 to the power of 2 is 36’. 43 = 4 · 4 · 4 = 64. We say that “4 cubed is 64”, or “4 to the power of 3 is 64” 25 = 2× 2 × 2 × 2 × 2 = 32. We say that ‘2 to the power of 5 is 32’. Most calculators have a button marked xy, or simply ˆ to calculate a power. Ensure that you are using the calculator correctly by verifying that 75 = 16807.

OPERATIONS AND RULES

2. Square roots

When 5 is squared we obtain 25. That is 52 = 25. The reverse of this process is called finding a square root. The square root of 25 is 5. This is written as  5 Note also that when −5 is squared we again obtain 25, that is (-5)2= 25. This means that 25 has another square root, −5. In general, a square root of a number is a number which when squared gives the original number. There are always two square roots of any positive number, one positive and one negative. Therefore, negative numbers do not possess any square roots.

3. Perfect squares    

A square number, also called a perfect square, is an integer that is the square of another integer. In other words, it is the product of some integer with itself. So, for example, 9 is a square number, since it can be written as 32

4. Cube roots and higher roots

The cube root of a number, is the number which when cubed gives the original number. For example, because  43= 64 we know that the cube root of 64 is 4, written  . All numbers, both positive and negative, possess a single cube root. Higher roots are defined in a similar way: because 25 = 32, the fifth root of 32 is 2.

EJERCICIOS
Potencias
Repaso potencias y raices
Operaciones combinadas

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FRACTIONS

When an object is divided into a number of equal parts, then each part is called a fraction. There are different ways of writing a fraction. For example, two fifths of an object can be written as a common fraction ® 2/5 a decimal ® 0.4 a percentage ® 40%        2               numerator says how many parts in the fraction        5               denominator says how many equal parts in the whole object Always remember: denominator can NEVER be 0. Why? Because you cannot divide by 0.

 Equivalent fractions

·         Two fractions are said to be equivalent when simplifying, both of them produces the same fraction written in its simplest terms. ·         Equivalent fractions are fractions with identical values. ·         To create a pair of equivalent fractions, you multiply (or divide, cancelling down) the top (numerator) and bottom (denominator) of a given fraction by the same number. ·         Two fractions are equivalent if the cross-products are the same.

OPERATIONS  WITH FRACTIONS  
Fraction operations

EJERCICIOS

Ordenar fracciones

Problems

Interactivo. Operaciones

Problemas interactivos 1

Problemas interactivos 2

Operaciones combinadas

Problemas con fracciones

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