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

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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

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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.

y=x²

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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.

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

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√2 can be written as a continuous fraction:

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