Given any number, you now know how to find its square. But, given the squared number, how do you find the original number?

## Example 3

By the end of this unit you should be able to:

• evaluate the squares, cubes and other powers of positive and negative numbers with or without your calculator;

• estimate square roots and calculate them using your calculator;

• describe the power notation for expressing numbers;

• use your calculator to find powers of numbers;

• multiply and divide powers of the same number;

• understand and apply negative powers, t
Author(s): The Open University

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook. Once you have completed the workbook and exercises return to this page and watch the video below, â€˜The arch never sleepsâ€™, which discusses a practical application of some of the ideas in workbook.

Click 'View document' to open the workbook (PDF, 0.8
Author(s): The Open University

### Activity 1 What does â€˜globalisationâ€™ mean to you?

Note down on paper or in your learning journalÂ  your first tho
Author(s): The Open University

Measuring the concentration of lead in the ice is called a direct measurement: the ice sample is melted and the water produced contains a very small but readily measured quantity of lead dust. A very accurate set of scales would be needed to measure it, but it is a directly measured quantity. There are also many indirect measurements that can be made using proxy data. The concept for using proxies is both simple and brilliant: one measured property allows inference about other states o
Author(s): The Open University

The polar bear has become an international climate change icon. But how much is known about this bear, its habitat and life? This unit will talk about the role of language, but by way of introduction how about the name of this bear? To me it is the polar bear; to a German it is an EisbÃ¤r (ice bear) and to a French person it is an ours blanc (white bear). In these three examples the bear is referred to as polar, white, or an ice bear â€“ eminently sensible. The Latin name for th
Author(s): The Open University

Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit:

The content acknowledged below is Proprietary and used under licence (not subject to Creative Commons licence). See Terms and Conditions.

## Unit image

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2. Enjoyed this? Browse through our host of free module materials on LearningSpace<
Author(s): The Open University

In economic terms, green consumerism is typically expressed using measures based on the willingness to pay (WTP) principle. As mentioned above, this takes two main forms: eco-taxation, in which environmental costs are estimated and added to the price of commodities (e.g. vehicles with high carbon emissions); and eco-labelling, in which products are labelled with relevant environmental information, such as is now required by the food industry and governments in many industrialised count
Author(s): The Open University

Evidence suggests that global temperature is beginning to rise. There are several factors that could cause this. Only one is affected by human activity.

Click on 'View document' to view a chart showing the rates of energy gain and loss by the Earth's surface and atmosphere

Earlier it was stated that three factors check population growth. These are predation, disease and insufficient food supply. For much of our history, our ancestorsâ€™ numbers were indeed limited by wars, disease and famine. The world population remained relatively stable until around 300 years ago. Then at the beginning of the 19th century (100 years after population growth started its geometric increase), the demographer Thomas Malthus predicted that population growth would outstrip food pro
Author(s): The Open University

Unfortunately, halting the disappearance of species cannot be achieved simply by measures such as putting fences around special habitats and asking people not to pick the flowers or disturb the breeding birds. Many species are vanishing because of pollution. You probably have a good understanding of the meaning of this term, but it is variously defined. The Open University has a course on environmental control and public health, in which pollution is defined as the introduction into th
Author(s): The Open University

I would like to turn now to the possible consequences of our use of energy for global climate change. Our pattern of energy use relies heavily on burning carbon-based fossil fuels, releasing carbon dioxide which spreads evenly around the globe and builds up slowly in the atmosphere. Carbon dioxide is a greenhouse gas, which means that it has the potential both to warm the atmosphere and to change our global climate. It is not the only greenhouse gas but is the most important of those e
Author(s): The Open University

But one striking example does not make an argument. To try to get a fuller and possibly fairer picture of energy use by domestic refrigerators I'd like also to look at the UK experience over the past few decades.

To start with it helps to have a feel for which parts of the UK economy use the most energy. The UK Department of Trade and Industry (DTI, 1998), identifies four main economic sectors: domestic (households), industry, services and transport.

In 2003 the domestic sector (h
Author(s): The Open University

A central concern of environmental studies is the relationship between technology and our environment: how people use technology to transform materials into forms which can meet our needs and wants. In the process of doing this we inevitably change the environment which provides these materials but which also supports all life.

A few moments ago I went to my fridge and took some milk out to add to a cup of coffee. I used this common example of a modern domestic appliance without a secon
Author(s): The Open University

The international level can be viewed as an arena of politics in its own right and not just as a context for states and other actors. If we think of the international world in this way, how should relations between states, and other actors on the international stage, be constructed? To what extent should those relations be regulated? We can ask whether relations between states, and states' policy making, should be dictated by allegedly universally shared human rights principles, or by other o
Author(s): The Open University

The aftermath of the 2004 Indian Ocean tsunami saw an unprecedented aid effort to assist the affected regions. In the early days after the disaster, pledges of financial assistance from overseas governments were often outstripped by the generosity of their own populaces. This was a case when ordinary people around the world saw and were moved by the tragic circumstances of others far away (Rose, 2006), and they responded with gifts of money and provisions, and even with offers of their own sk
Author(s): The Open University

Several attempts have been made to form a united front of developing countries to negotiate a better deal at the WTO. They have met with little success because there are substantial conflicts of interest between them, for example between agricultural importers and exporters, and between small countries and those larger developing countries that have been able individually to use the lure of opening their markets to get a better deal from developed countries. Conflicts of interest arise too be
Author(s): The Open University

## Course Team Chair of Production

Gillian Rose, Professor of Cultural Geography

## Course Team Chair of Presentation

Chris Brook, Senior Lecturer in Geography

## External Assessor

Peter Jackson, Professor of Human Geography, University of Sheffield

## Author(s): The Open UniversityLicense informationRelated contentExcept for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

Global markets for manufactured goods, as opposed to, say, primary commodities such as oil and timber, arose largely in the second half of the twentieth century as trade between countries intensified. The lowering of transport costs and the relative fall in trade barriers enabled firms in one country to compete wit
Author(s): The Open University

The activities and resources in this section engage you in an interdisciplinary investigation of your personal ecology by looking at a range of temporal, spatial, and organisational scales â€“ from the personal to the global, from the short term to the long term. The aim is to gather evidence to he
Author(s): The Open University