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Secondary Magazine - Issue 15: Focus on Square Roots

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 28 July 2008 by ncetm_administrator
Updated on 30 July 2008 by ncetm_administrator

Secondary Magazine

Welcome to issue 15 of the NCETM Secondary Magazine. Fortnightly features include: The Interview, Around the regions, An idea for the classroom, 5 things to do, The Diary and Focus on. Issue 15 focuses on square roots.
 Focus on… Square Roots

In mathematics, a square root of a number x is a number r such that r2 = x, or in words, a number r whose square (the result of multiplying the number by itself) is x. Every non-negative real number x has a unique non-negative square root, called the principal square root and denoted with a radical symbol as √x. For example, the principal square root of 9 is 3, denoted √9 = 3, because 32 = 3 × 3 = 9. If otherwise unqualified, "the square root" of a number refers to the principal square root: the square root of 2 is approximately 1.4142. Wikipedia 

Every positive number x has two square roots. One of them is √x, which is positive, and the other −√x, which is negative. Together, these two roots are denoted ±√x.


Square roots of integers that are not perfect squares are always irrational numbers; numbers that cannot be written as a ratio of two integers. √2 is an irrational number.
Click here to find out more.
Watch Donald in Mathmagic land and see the trees with square roots.
The square of any positive or negative number is positive, and the square of 0 is 0. Therefore, no negative number can have a real square root. However, it is possible to work with a larger set of numbers, called the complex numbers, that does contain solutions to the square root of a negative number. This is done by introducing a new number, denoted by i and called the imaginary unit, which is defined such that i2 = −1. Using this notation, we can think of i as the square root of −1, but notice that we also have (−i)2 = i2 = −1 and so −i is also a square root of −1. Wikipedia

√2 can be written as a continuous fraction:

Click here to read about Lesson Account 34 - Using Pythagoras' Theorem.

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Secondary Focus - Portal Tour  
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Browse... Issue 15
The Interview, Around the regions, An idea for the classroom, 5 things to do, The Diary, Homepage

Browse... PD Activities
Self-evaluation, Why do we teach mathematics?, Learning mathematics in my school, Pathways and options at KS3 to KS5, Mathematical Vocabulary, Revision, Group Work, C/D Borderline, Planning teaching and learning, Technology for learning

Are Mathematicians Geeks?


The Diary - real issues in the life of a fictional Subject Leader


An idea for the classroom


5 things to do


The Interview - Dan Bowles


Around the regions - news, views and updates from the NCETM Regional Coordinators


Explore the Secondary Forum

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