Mathematics for science and technology
Mathematics for science and technology

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Mathematics for science and technology

1.4 Roots and fractional indices

To see what fractional indices mean in practice a good place to start is with this example:

open two super one divided by two close squared

Using Rule 3 and 1 this can be written as follows:

multiline equation row 1 open two super one divided by two close squared equals two super one divided by two multiplication two super one divided by two row 2 equals two super open one divided by two plus one divided by two close row 3 equals two super one row 4 equals two

This shows that 21/2 is a way to represent the square root of 2. Since Square root of two multiplication Square root of two equals two.

Extending this a1/3 is the cube root of a and can be written as root of order three over three. a1/4 is the fourth root of a, written as root of order four over four.

 

So it follows that:

a1/n is the nth root of a and can be written as root of order n over n.

If you use Rule 3 to write ap/q as open a super p close super one divided by q, you should now be able to see that ap/q is the qth root of ap which is written as root of order q over q.

So, equation left hand side a super super p divided by q equals right hand side root of order q over q

Rules 1, 2, and 3 all work with fractional indices.

Before moving on to another topic, you’ll learn what the power of zero means.

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